10 79

10_78

10_80

(KnotPlot image)

See the full Rolfsen Knot Table.

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[edit 10 79 Quick Notes]

[edit 10 79 Further Notes and Views]

Knot presentations

Planar diagram presentation	X₆₂₇₁ X₈₄₉₃ X_12,6,13,5 X_18,13,19,14 X_16,9,17,10 X_10,17,11,18 X_20,15,1,16 X_14,19,15,20 X₂₈₃₇ X_4,12,5,11
Gauss code	1, -9, 2, -10, 3, -1, 9, -2, 5, -6, 10, -3, 4, -8, 7, -5, 6, -4, 8, -7
Dowker-Thistlethwaite code	6 8 12 2 16 4 18 20 10 14
Conway Notation	[(3,2)(3,2)]

Minimum Braid Representative

A Morse Link Presentation

An Arc Presentation

Length is 10, width is 3,

Braid index is 3

[{9, 12}, {3, 11}, {12, 10}, {2, 6}, {1, 3}, {4, 7}, {5, 2}, {6, 8}, {7, 9}, {8, 4}, {11, 5}, {10, 1}]

[edit Notes on presentations of 10 79]

Computer Talk

The above data is available with the Mathematica package KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:= AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`

Loading KnotTheory` version of May 31, 2006, 14:15:20.091.

Read more at http://katlas.org/wiki/KnotTheory.

In[3]:= K = Knot["10 79"];

In[4]:= PD[K]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[4]= X₆₂₇₁ X₈₄₉₃ X_12,6,13,5 X_18,13,19,14 X_16,9,17,10 X_10,17,11,18 X_20,15,1,16 X_14,19,15,20 X₂₈₃₇ X_4,12,5,11

In[5]:= GaussCode[K]

Out[5]= 1, -9, 2, -10, 3, -1, 9, -2, 5, -6, 10, -3, 4, -8, 7, -5, 6, -4, 8, -7

In[6]:= DTCode[K]

Out[6]= 6 8 12 2 16 4 18 20 10 14

(The path below may be different on your system)

In[7]:= AppendTo[$Path, "C:/bin/LinKnot/"];

In[8]:= ConwayNotation[K]

Out[8]= [(3,2)(3,2)]

In[9]:= br = BR[K]

KnotTheory::credits: The minimum braids representing the knots with up to 10 crossings were provided by Thomas Gittings. See arXiv:math.GT/0401051.

Out[9]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \textrm{BR}(3,\{-1,-1,-1,2,2,-1,-1,2,2,2\})}

In[10]:= {First[br], Crossings[br], BraidIndex[K]}

KnotTheory::credits: The braid index data known to KnotTheory` is taken from Charles Livingston's http://www.indiana.edu/~knotinfo/.

KnotTheory::loading: Loading precomputed data in IndianaData`.

Out[10]= { 3, 10, 3 }

In[11]:= Show[BraidPlot[br]]

Out[11]= -Graphics-

In[12]:= Show[DrawMorseLink[K]]

KnotTheory::credits: "MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005."

KnotTheory::credits: "DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005."

Out[12]= -Graphics-

In[13]:= ap = ArcPresentation[K]

Out[13]= ArcPresentation[{9, 12}, {3, 11}, {12, 10}, {2, 6}, {1, 3}, {4, 7}, {5, 2}, {6, 8}, {7, 9}, {8, 4}, {11, 5}, {10, 1}]

In[14]:= Draw[ap]

Out[14]= -Graphics-

Three dimensional invariants

Symmetry type	Negative amphicheiral
Unknotting number	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{2,3\}}
3-genus	4
Bridge index	3
Super bridge index	Missing
Nakanishi index	1
Maximal Thurston-Bennequin number	[-6][-6]
Hyperbolic Volume	12.5403
A-Polynomial	See Data:10 79/A-polynomial

[edit Notes for 10 79's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1}
Topological 4 genus	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1}
Concordance genus	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4}
Rasmussen s-Invariant	0

[edit Notes for 10 79's four dimensional invariants]

Polynomial invariants

Alexander polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^4-3 t^3+7 t^2-12 t+15-12 t^{-1} +7 t^{-2} -3 t^{-3} + t^{-4} }
Conway polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^8+5 z^6+9 z^4+5 z^2+1}
2nd Alexander ideal (db, data sources)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{1\}}
Determinant and Signature	{ 61, 0 }
Jones polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^5+2 q^4-5 q^3+8 q^2-9 q+11-9 q^{-1} +8 q^{-2} -5 q^{-3} +2 q^{-4} - q^{-5} }
HOMFLY-PT polynomial (db, data sources)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^8-a^2 z^6-z^6 a^{-2} +7 z^6-5 a^2 z^4-5 z^4 a^{-2} +19 z^4-9 a^2 z^2-9 z^2 a^{-2} +23 z^2-5 a^2-5 a^{-2} +11}
Kauffman polynomial (db, data sources)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a z^9+z^9 a^{-1} +3 a^2 z^8+3 z^8 a^{-2} +6 z^8+3 a^3 z^7+4 a z^7+4 z^7 a^{-1} +3 z^7 a^{-3} +2 a^4 z^6-7 a^2 z^6-7 z^6 a^{-2} +2 z^6 a^{-4} -18 z^6+a^5 z^5-6 a^3 z^5-15 a z^5-15 z^5 a^{-1} -6 z^5 a^{-3} +z^5 a^{-5} -4 a^4 z^4+12 a^2 z^4+12 z^4 a^{-2} -4 z^4 a^{-4} +32 z^4-3 a^5 z^3+4 a^3 z^3+22 a z^3+22 z^3 a^{-1} +4 z^3 a^{-3} -3 z^3 a^{-5} +a^4 z^2-13 a^2 z^2-13 z^2 a^{-2} +z^2 a^{-4} -28 z^2+2 a^5 z-2 a^3 z-11 a z-11 z a^{-1} -2 z a^{-3} +2 z a^{-5} +5 a^2+5 a^{-2} +11}
The A2 invariant	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{14}-3 q^{10}+5 q^2+1+5 q^{-2} -3 q^{-10} - q^{-14} }
The G2 invariant	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{80}-q^{78}+3 q^{76}-4 q^{74}+4 q^{72}-3 q^{70}-q^{68}+8 q^{66}-15 q^{64}+21 q^{62}-23 q^{60}+16 q^{58}-4 q^{56}-18 q^{54}+44 q^{52}-63 q^{50}+64 q^{48}-47 q^{46}+q^{44}+45 q^{42}-88 q^{40}+101 q^{38}-82 q^{36}+29 q^{34}+29 q^{32}-79 q^{30}+87 q^{28}-58 q^{26}+4 q^{24}+50 q^{22}-75 q^{20}+60 q^{18}-7 q^{16}-53 q^{14}+105 q^{12}-113 q^{10}+85 q^8-15 q^6-59 q^4+126 q^2-143+126 q^{-2} -59 q^{-4} -15 q^{-6} +85 q^{-8} -113 q^{-10} +105 q^{-12} -53 q^{-14} -7 q^{-16} +60 q^{-18} -75 q^{-20} +50 q^{-22} +4 q^{-24} -58 q^{-26} +87 q^{-28} -79 q^{-30} +29 q^{-32} +29 q^{-34} -82 q^{-36} +101 q^{-38} -88 q^{-40} +45 q^{-42} + q^{-44} -47 q^{-46} +64 q^{-48} -63 q^{-50} +44 q^{-52} -18 q^{-54} -4 q^{-56} +16 q^{-58} -23 q^{-60} +21 q^{-62} -15 q^{-64} +8 q^{-66} - q^{-68} -3 q^{-70} +4 q^{-72} -4 q^{-74} +3 q^{-76} - q^{-78} + q^{-80} }

Further Quantum Invariants

Further quantum knot invariants for 10_79.

A1 Invariants.

Weight	Invariant
1	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{11}+q^9-3 q^7+3 q^5-q^3+2 q+2 q^{-1} - q^{-3} +3 q^{-5} -3 q^{-7} + q^{-9} - q^{-11} }
2	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{32}-q^{30}+4 q^{26}-5 q^{24}-4 q^{22}+12 q^{20}-7 q^{18}-14 q^{16}+18 q^{14}-19 q^{10}+13 q^8+8 q^6-12 q^4+2 q^2+11+2 q^{-2} -12 q^{-4} +8 q^{-6} +13 q^{-8} -19 q^{-10} +18 q^{-14} -14 q^{-16} -7 q^{-18} +12 q^{-20} -4 q^{-22} -5 q^{-24} +4 q^{-26} - q^{-30} + q^{-32} }
3	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{63}+q^{61}-q^{57}-q^{55}+4 q^{53}+2 q^{51}-7 q^{49}-5 q^{47}+15 q^{45}+14 q^{43}-19 q^{41}-33 q^{39}+20 q^{37}+55 q^{35}-9 q^{33}-76 q^{31}-21 q^{29}+91 q^{27}+46 q^{25}-86 q^{23}-78 q^{21}+70 q^{19}+91 q^{17}-45 q^{15}-98 q^{13}+23 q^{11}+87 q^9+8 q^7-70 q^5-27 q^3+52 q+52 q^{-1} -27 q^{-3} -70 q^{-5} +8 q^{-7} +87 q^{-9} +23 q^{-11} -98 q^{-13} -45 q^{-15} +91 q^{-17} +70 q^{-19} -78 q^{-21} -86 q^{-23} +46 q^{-25} +91 q^{-27} -21 q^{-29} -76 q^{-31} -9 q^{-33} +55 q^{-35} +20 q^{-37} -33 q^{-39} -19 q^{-41} +14 q^{-43} +15 q^{-45} -5 q^{-47} -7 q^{-49} +2 q^{-51} +4 q^{-53} - q^{-55} - q^{-57} + q^{-61} - q^{-63} }
4	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{104}-q^{102}+q^{98}-2 q^{96}+2 q^{94}-3 q^{92}+q^{90}+6 q^{88}-7 q^{86}-q^{84}-12 q^{82}+6 q^{80}+33 q^{78}+2 q^{76}-14 q^{74}-66 q^{72}-23 q^{70}+85 q^{68}+91 q^{66}+46 q^{64}-158 q^{62}-192 q^{60}+20 q^{58}+220 q^{56}+307 q^{54}-74 q^{52}-402 q^{50}-304 q^{48}+115 q^{46}+599 q^{44}+302 q^{42}-334 q^{40}-635 q^{38}-276 q^{36}+565 q^{34}+644 q^{32}+28 q^{30}-629 q^{28}-593 q^{26}+245 q^{24}+644 q^{22}+325 q^{20}-350 q^{18}-590 q^{16}-59 q^{14}+404 q^{12}+399 q^{10}-64 q^8-411 q^6-239 q^4+158 q^2+385+158 q^{-2} -239 q^{-4} -411 q^{-6} -64 q^{-8} +399 q^{-10} +404 q^{-12} -59 q^{-14} -590 q^{-16} -350 q^{-18} +325 q^{-20} +644 q^{-22} +245 q^{-24} -593 q^{-26} -629 q^{-28} +28 q^{-30} +644 q^{-32} +565 q^{-34} -276 q^{-36} -635 q^{-38} -334 q^{-40} +302 q^{-42} +599 q^{-44} +115 q^{-46} -304 q^{-48} -402 q^{-50} -74 q^{-52} +307 q^{-54} +220 q^{-56} +20 q^{-58} -192 q^{-60} -158 q^{-62} +46 q^{-64} +91 q^{-66} +85 q^{-68} -23 q^{-70} -66 q^{-72} -14 q^{-74} +2 q^{-76} +33 q^{-78} +6 q^{-80} -12 q^{-82} - q^{-84} -7 q^{-86} +6 q^{-88} + q^{-90} -3 q^{-92} +2 q^{-94} -2 q^{-96} + q^{-98} - q^{-102} + q^{-104} }
5	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{155}+q^{153}-q^{149}+2 q^{147}+q^{145}-3 q^{143}+q^{139}-2 q^{137}+5 q^{135}+9 q^{133}-5 q^{131}-12 q^{129}-13 q^{127}-9 q^{125}+17 q^{123}+47 q^{121}+36 q^{119}-20 q^{117}-84 q^{115}-110 q^{113}-31 q^{111}+120 q^{109}+232 q^{107}+174 q^{105}-82 q^{103}-376 q^{101}-436 q^{99}-124 q^{97}+417 q^{95}+797 q^{93}+587 q^{91}-230 q^{89}-1087 q^{87}-1252 q^{85}-365 q^{83}+1081 q^{81}+1983 q^{79}+1368 q^{77}-589 q^{75}-2447 q^{73}-2568 q^{71}-506 q^{69}+2363 q^{67}+3692 q^{65}+1995 q^{63}-1644 q^{61}-4278 q^{59}-3550 q^{57}+293 q^{55}+4214 q^{53}+4767 q^{51}+1252 q^{49}-3436 q^{47}-5320 q^{45}-2715 q^{43}+2227 q^{41}+5174 q^{39}+3668 q^{37}-874 q^{35}-4452 q^{33}-4047 q^{31}-264 q^{29}+3401 q^{27}+3869 q^{25}+1072 q^{23}-2321 q^{21}-3380 q^{19}-1467 q^{17}+1398 q^{15}+2745 q^{13}+1651 q^{11}-705 q^9-2228 q^7-1719 q^5+218 q^3+1879 q+1879 q^{-1} +218 q^{-3} -1719 q^{-5} -2228 q^{-7} -705 q^{-9} +1651 q^{-11} +2745 q^{-13} +1398 q^{-15} -1467 q^{-17} -3380 q^{-19} -2321 q^{-21} +1072 q^{-23} +3869 q^{-25} +3401 q^{-27} -264 q^{-29} -4047 q^{-31} -4452 q^{-33} -874 q^{-35} +3668 q^{-37} +5174 q^{-39} +2227 q^{-41} -2715 q^{-43} -5320 q^{-45} -3436 q^{-47} +1252 q^{-49} +4767 q^{-51} +4214 q^{-53} +293 q^{-55} -3550 q^{-57} -4278 q^{-59} -1644 q^{-61} +1995 q^{-63} +3692 q^{-65} +2363 q^{-67} -506 q^{-69} -2568 q^{-71} -2447 q^{-73} -589 q^{-75} +1368 q^{-77} +1983 q^{-79} +1081 q^{-81} -365 q^{-83} -1252 q^{-85} -1087 q^{-87} -230 q^{-89} +587 q^{-91} +797 q^{-93} +417 q^{-95} -124 q^{-97} -436 q^{-99} -376 q^{-101} -82 q^{-103} +174 q^{-105} +232 q^{-107} +120 q^{-109} -31 q^{-111} -110 q^{-113} -84 q^{-115} -20 q^{-117} +36 q^{-119} +47 q^{-121} +17 q^{-123} -9 q^{-125} -13 q^{-127} -12 q^{-129} -5 q^{-131} +9 q^{-133} +5 q^{-135} -2 q^{-137} + q^{-139} -3 q^{-143} + q^{-145} +2 q^{-147} - q^{-149} + q^{-153} - q^{-155} }
6	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{216}-q^{214}+q^{210}-2 q^{208}-q^{206}+6 q^{202}-2 q^{200}-5 q^{198}+3 q^{196}-5 q^{194}-4 q^{192}+2 q^{190}+23 q^{188}+9 q^{186}-14 q^{184}-8 q^{182}-31 q^{180}-33 q^{178}-5 q^{176}+79 q^{174}+90 q^{172}+41 q^{170}-133 q^{166}-221 q^{164}-192 q^{162}+77 q^{160}+318 q^{158}+424 q^{156}+397 q^{154}-38 q^{152}-612 q^{150}-1014 q^{148}-724 q^{146}+18 q^{144}+1001 q^{142}+1846 q^{140}+1590 q^{138}+215 q^{136}-1824 q^{134}-3053 q^{132}-2931 q^{130}-871 q^{128}+2618 q^{126}+5189 q^{124}+5175 q^{122}+1689 q^{120}-3379 q^{118}-7953 q^{116}-8542 q^{114}-3498 q^{112}+4686 q^{110}+11716 q^{108}+12553 q^{106}+6128 q^{104}-6006 q^{102}-16477 q^{100}-17997 q^{98}-8512 q^{96}+7925 q^{94}+21510 q^{92}+24060 q^{90}+10906 q^{88}-10682 q^{86}-27701 q^{84}-29020 q^{82}-12009 q^{80}+13861 q^{78}+33801 q^{76}+32854 q^{74}+11153 q^{72}-18682 q^{70}-37998 q^{68}-33953 q^{66}-8484 q^{64}+23696 q^{62}+40371 q^{60}+31753 q^{58}+3049 q^{56}-27098 q^{54}-39538 q^{52}-26785 q^{50}+3146 q^{48}+28958 q^{46}+35370 q^{44}+18968 q^{42}-8079 q^{40}-28122 q^{38}-28875 q^{36}-10823 q^{34}+11680 q^{32}+24759 q^{30}+20638 q^{28}+4229 q^{26}-13088 q^{24}-20018 q^{22}-13027 q^{20}+972 q^{18}+12802 q^{16}+14704 q^{14}+7084 q^{12}-4556 q^{10}-11920 q^8-10508 q^6-2176 q^4+7427 q^2+11325+7427 q^{-2} -2176 q^{-4} -10508 q^{-6} -11920 q^{-8} -4556 q^{-10} +7084 q^{-12} +14704 q^{-14} +12802 q^{-16} +972 q^{-18} -13027 q^{-20} -20018 q^{-22} -13088 q^{-24} +4229 q^{-26} +20638 q^{-28} +24759 q^{-30} +11680 q^{-32} -10823 q^{-34} -28875 q^{-36} -28122 q^{-38} -8079 q^{-40} +18968 q^{-42} +35370 q^{-44} +28958 q^{-46} +3146 q^{-48} -26785 q^{-50} -39538 q^{-52} -27098 q^{-54} +3049 q^{-56} +31753 q^{-58} +40371 q^{-60} +23696 q^{-62} -8484 q^{-64} -33953 q^{-66} -37998 q^{-68} -18682 q^{-70} +11153 q^{-72} +32854 q^{-74} +33801 q^{-76} +13861 q^{-78} -12009 q^{-80} -29020 q^{-82} -27701 q^{-84} -10682 q^{-86} +10906 q^{-88} +24060 q^{-90} +21510 q^{-92} +7925 q^{-94} -8512 q^{-96} -17997 q^{-98} -16477 q^{-100} -6006 q^{-102} +6128 q^{-104} +12553 q^{-106} +11716 q^{-108} +4686 q^{-110} -3498 q^{-112} -8542 q^{-114} -7953 q^{-116} -3379 q^{-118} +1689 q^{-120} +5175 q^{-122} +5189 q^{-124} +2618 q^{-126} -871 q^{-128} -2931 q^{-130} -3053 q^{-132} -1824 q^{-134} +215 q^{-136} +1590 q^{-138} +1846 q^{-140} +1001 q^{-142} +18 q^{-144} -724 q^{-146} -1014 q^{-148} -612 q^{-150} -38 q^{-152} +397 q^{-154} +424 q^{-156} +318 q^{-158} +77 q^{-160} -192 q^{-162} -221 q^{-164} -133 q^{-166} +41 q^{-170} +90 q^{-172} +79 q^{-174} -5 q^{-176} -33 q^{-178} -31 q^{-180} -8 q^{-182} -14 q^{-184} +9 q^{-186} +23 q^{-188} +2 q^{-190} -4 q^{-192} -5 q^{-194} +3 q^{-196} -5 q^{-198} -2 q^{-200} +6 q^{-202} - q^{-206} -2 q^{-208} + q^{-210} - q^{-214} + q^{-216} }

A2 Invariants.

Weight	Invariant
1,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{14}-3 q^{10}+5 q^2+1+5 q^{-2} -3 q^{-10} - q^{-14} }
1,1	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{44}-2 q^{42}+6 q^{40}-12 q^{38}+25 q^{36}-42 q^{34}+68 q^{32}-106 q^{30}+155 q^{28}-214 q^{26}+276 q^{24}-332 q^{22}+363 q^{20}-368 q^{18}+312 q^{16}-224 q^{14}+67 q^{12}+102 q^{10}-294 q^8+476 q^6-610 q^4+724 q^2-734+724 q^{-2} -610 q^{-4} +476 q^{-6} -294 q^{-8} +102 q^{-10} +67 q^{-12} -224 q^{-14} +312 q^{-16} -368 q^{-18} +363 q^{-20} -332 q^{-22} +276 q^{-24} -214 q^{-26} +155 q^{-28} -106 q^{-30} +68 q^{-32} -42 q^{-34} +25 q^{-36} -12 q^{-38} +6 q^{-40} -2 q^{-42} + q^{-44} }
2,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{38}+q^{34}+3 q^{32}-2 q^{28}+3 q^{26}-7 q^{22}-7 q^{20}+q^{18}-q^{16}-13 q^{14}-2 q^{12}+5 q^{10}-4 q^8-q^6+12 q^4+11 q^2+6+11 q^{-2} +12 q^{-4} - q^{-6} -4 q^{-8} +5 q^{-10} -2 q^{-12} -13 q^{-14} - q^{-16} + q^{-18} -7 q^{-20} -7 q^{-22} +3 q^{-26} -2 q^{-28} +3 q^{-32} + q^{-34} + q^{-38} }

A3 Invariants.

Weight	Invariant
0,1,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{34}-q^{32}+q^{30}+3 q^{28}-4 q^{26}+q^{24}+7 q^{22}-12 q^{20}+9 q^{16}-20 q^{14}-5 q^{12}+7 q^{10}-13 q^8-q^6+15 q^4+10 q^2+10+10 q^{-2} +15 q^{-4} - q^{-6} -13 q^{-8} +7 q^{-10} -5 q^{-12} -20 q^{-14} +9 q^{-16} -12 q^{-20} +7 q^{-22} + q^{-24} -4 q^{-26} +3 q^{-28} + q^{-30} - q^{-32} + q^{-34} }
1,0,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{17}-4 q^{13}-4 q^9+q^7+5 q^3+5 q+5 q^{-1} +5 q^{-3} + q^{-7} -4 q^{-9} -4 q^{-13} - q^{-17} }
1,0,1	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{56}-2 q^{54}+5 q^{52}-5 q^{50}+2 q^{48}+10 q^{46}-24 q^{44}+34 q^{42}-24 q^{40}-14 q^{38}+67 q^{36}-113 q^{34}+108 q^{32}-22 q^{30}-107 q^{28}+245 q^{26}-276 q^{24}+187 q^{22}+8 q^{20}-265 q^{18}+360 q^{16}-401 q^{14}+173 q^{12}+9 q^{10}-205 q^8+256 q^6-120 q^4+85 q^2+71+85 q^{-2} -120 q^{-4} +256 q^{-6} -205 q^{-8} +9 q^{-10} +173 q^{-12} -401 q^{-14} +360 q^{-16} -265 q^{-18} +8 q^{-20} +187 q^{-22} -276 q^{-24} +245 q^{-26} -107 q^{-28} -22 q^{-30} +108 q^{-32} -113 q^{-34} +67 q^{-36} -14 q^{-38} -24 q^{-40} +34 q^{-42} -24 q^{-44} +10 q^{-46} +2 q^{-48} -5 q^{-50} +5 q^{-52} -2 q^{-54} + q^{-56} }

A4 Invariants.

Weight

Invariant

0,1,0,0

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{40}+q^{36}+4 q^{34}+q^{32}+8 q^{28}-q^{26}-8 q^{24}+q^{22}-2 q^{20}-22 q^{18}-19 q^{16}-7 q^{14}-15 q^{12}-21 q^{10}+3 q^8+23 q^6+9 q^4+26 q^2+46+26 q^{-2} +9 q^{-4} +23 q^{-6} +3 q^{-8} -21 q^{-10} -15 q^{-12} -7 q^{-14} -19 q^{-16} -22 q^{-18} -2 q^{-20} + q^{-22} -8 q^{-24} - q^{-26} +8 q^{-28} + q^{-32} +4 q^{-34} + q^{-36} + q^{-40} }

1,0,0,0

-q^{20}-4q^{16}-q^{14}-4q^{12}-3q^{10}+6q^{4}+5q^{2}+9+5q^{-2}+6q^{-4}-3q^{-10}-4q^{-12}-q^{-14}-4q^{-16}-q^{-20}

B2 Invariants.

Weight

Invariant

0,1

-q^{34}+q^{32}-3q^{30}+5q^{28}-8q^{26}+11q^{24}-15q^{22}+16q^{20}-18q^{18}+15q^{16}-12q^{14}+5q^{12}+3q^{10}-11q^{8}+21q^{6}-25q^{4}+34q^{2}-32+34q^{-2}-25q^{-4}+21q^{-6}-11q^{-8}+3q^{-10}+5q^{-12}-12q^{-14}+15q^{-16}-18q^{-18}+16q^{-20}-15q^{-22}+11q^{-24}-8q^{-26}+5q^{-28}-3q^{-30}+q^{-32}-q^{-34}

1,0

q^{56}-q^{52}-q^{50}+2q^{48}+4q^{46}-6q^{42}-4q^{40}+6q^{38}+11q^{36}-3q^{34}-16q^{32}-8q^{30}+13q^{28}+13q^{26}-10q^{24}-21q^{22}-4q^{20}+15q^{18}+6q^{16}-13q^{14}-11q^{12}+9q^{10}+13q^{8}-8q^{4}+7q^{2}+17+7q^{-2}-8q^{-4}+13q^{-8}+9q^{-10}-11q^{-12}-13q^{-14}+6q^{-16}+15q^{-18}-4q^{-20}-21q^{-22}-10q^{-24}+13q^{-26}+13q^{-28}-8q^{-30}-16q^{-32}-3q^{-34}+11q^{-36}+6q^{-38}-4q^{-40}-6q^{-42}+4q^{-46}+2q^{-48}-q^{-50}-q^{-52}+q^{-56}

D4 Invariants.

Weight

Invariant

1,0,0,0

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{46}-q^{44}+2 q^{42}-2 q^{40}+5 q^{38}-6 q^{36}+7 q^{34}-9 q^{32}+12 q^{30}-14 q^{28}+12 q^{26}-14 q^{24}+11 q^{22}-15 q^{20}-q^{18}-10 q^{16}-7 q^{14}+q^{12}-17 q^{10}+16 q^8-12 q^6+36 q^4-11 q^2+40-11 q^{-2} +36 q^{-4} -12 q^{-6} +16 q^{-8} -17 q^{-10} + q^{-12} -7 q^{-14} -10 q^{-16} - q^{-18} -15 q^{-20} +11 q^{-22} -14 q^{-24} +12 q^{-26} -14 q^{-28} +12 q^{-30} -9 q^{-32} +7 q^{-34} -6 q^{-36} +5 q^{-38} -2 q^{-40} +2 q^{-42} - q^{-44} + q^{-46} }

G2 Invariants.

Weight

Invariant

1,0

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{80}-q^{78}+3 q^{76}-4 q^{74}+4 q^{72}-3 q^{70}-q^{68}+8 q^{66}-15 q^{64}+21 q^{62}-23 q^{60}+16 q^{58}-4 q^{56}-18 q^{54}+44 q^{52}-63 q^{50}+64 q^{48}-47 q^{46}+q^{44}+45 q^{42}-88 q^{40}+101 q^{38}-82 q^{36}+29 q^{34}+29 q^{32}-79 q^{30}+87 q^{28}-58 q^{26}+4 q^{24}+50 q^{22}-75 q^{20}+60 q^{18}-7 q^{16}-53 q^{14}+105 q^{12}-113 q^{10}+85 q^8-15 q^6-59 q^4+126 q^2-143+126 q^{-2} -59 q^{-4} -15 q^{-6} +85 q^{-8} -113 q^{-10} +105 q^{-12} -53 q^{-14} -7 q^{-16} +60 q^{-18} -75 q^{-20} +50 q^{-22} +4 q^{-24} -58 q^{-26} +87 q^{-28} -79 q^{-30} +29 q^{-32} +29 q^{-34} -82 q^{-36} +101 q^{-38} -88 q^{-40} +45 q^{-42} + q^{-44} -47 q^{-46} +64 q^{-48} -63 q^{-50} +44 q^{-52} -18 q^{-54} -4 q^{-56} +16 q^{-58} -23 q^{-60} +21 q^{-62} -15 q^{-64} +8 q^{-66} - q^{-68} -3 q^{-70} +4 q^{-72} -4 q^{-74} +3 q^{-76} - q^{-78} + q^{-80} }

.

Computer Talk

The above data is available with the Mathematica package KnotTheory`, as shown in the (simulated) Mathematica session below. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting. This Mathematica session is also available (albeit only for the knot 5_2) as the notebook PolynomialInvariantsSession.nb.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:= AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`

Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.

In[3]:= K = Knot["10 79"];

In[4]:= Alexander[K][t]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[4]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^4-3 t^3+7 t^2-12 t+15-12 t^{-1} +7 t^{-2} -3 t^{-3} + t^{-4} }

In[5]:= Conway[K][z]

Out[5]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^8+5 z^6+9 z^4+5 z^2+1}

In[6]:= Alexander[K, 2][t]

KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.

Out[6]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{1\}}

In[7]:= {KnotDet[K], KnotSignature[K]}

Out[7]= { 61, 0 }

In[8]:= Jones[K][q]

KnotTheory::loading: Loading precomputed data in Jones4Knots`.

Out[8]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^5+2 q^4-5 q^3+8 q^2-9 q+11-9 q^{-1} +8 q^{-2} -5 q^{-3} +2 q^{-4} - q^{-5} }

In[9]:= HOMFLYPT[K][a, z]

KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.

Out[9]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^8-a^2 z^6-z^6 a^{-2} +7 z^6-5 a^2 z^4-5 z^4 a^{-2} +19 z^4-9 a^2 z^2-9 z^2 a^{-2} +23 z^2-5 a^2-5 a^{-2} +11}

In[10]:= Kauffman[K][a, z]

KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.

Out[10]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a z^9+z^9 a^{-1} +3 a^2 z^8+3 z^8 a^{-2} +6 z^8+3 a^3 z^7+4 a z^7+4 z^7 a^{-1} +3 z^7 a^{-3} +2 a^4 z^6-7 a^2 z^6-7 z^6 a^{-2} +2 z^6 a^{-4} -18 z^6+a^5 z^5-6 a^3 z^5-15 a z^5-15 z^5 a^{-1} -6 z^5 a^{-3} +z^5 a^{-5} -4 a^4 z^4+12 a^2 z^4+12 z^4 a^{-2} -4 z^4 a^{-4} +32 z^4-3 a^5 z^3+4 a^3 z^3+22 a z^3+22 z^3 a^{-1} +4 z^3 a^{-3} -3 z^3 a^{-5} +a^4 z^2-13 a^2 z^2-13 z^2 a^{-2} +z^2 a^{-4} -28 z^2+2 a^5 z-2 a^3 z-11 a z-11 z a^{-1} -2 z a^{-3} +2 z a^{-5} +5 a^2+5 a^{-2} +11}

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

Same Jones Polynomial (up to mirroring, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q\leftrightarrow q^{-1}} ): {}

Computer Talk

The above data is available with the Mathematica package KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:= AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`

Loading KnotTheory` version of May 31, 2006, 14:15:20.091.

In[3]:= K = Knot["10 79"];

In[4]:= {A = Alexander[K][t], J = Jones[K][q]}

KnotTheory::loading: Loading precomputed data in PD4Knots`.

KnotTheory::loading: Loading precomputed data in Jones4Knots`.

Out[4]= { Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^4-3 t^3+7 t^2-12 t+15-12 t^{-1} +7 t^{-2} -3 t^{-3} + t^{-4} } , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^5+2 q^4-5 q^3+8 q^2-9 q+11-9 q^{-1} +8 q^{-2} -5 q^{-3} +2 q^{-4} - q^{-5} } }

In[5]:= DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]

KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.

KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.

Out[5]= {}

In[6]:= DeleteCases[ Select[ AllKnots[], (J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) & ], K ]

KnotTheory::loading: Loading precomputed data in Jones4Knots11`.

Out[6]= {}

Vassiliev invariants

V₂ and V₃:

(5, 0)

V_2,1 through V_6,9:

V_2,1

V_3,1

V_4,1

V_4,2

V_4,3

V_5,1

V_5,2

V_5,3

V_5,4

V_6,1

V_6,2

V_6,3

V_6,4

V_6,5

V_6,6

V_6,7

V_6,8

V_6,9

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 20}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 200}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{694}{3}}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{74}{3}}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4000}{3}}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{13880}{3}}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1480}{3}}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{27247}{6}}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1154}{3}}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{11678}{9}}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1045}{18}}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{559}{6}}

V_2,1 through V_6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V₂ and V₃.

Khovanov Homology

The coefficients of the monomials Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^rq^j} are shown, along with their alternating sums Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \chi} (fixed Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j} , alternation over Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} ). The squares with yellow highlighting are those on the "critical diagonals", where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j-2r=s+1} or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j-2r=s-1} , where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle s=} 0 is the signature of 10 79. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

\		r
	\
j		\

-5

-4

-3

-2

-1

0

1

2

3

4

5

χ

11

1

-1

9

1

7

4

1

-3

5

4

1

3

5

4

-1

1

6

4

2

-1

4

6

2

-3

4

5

-1

-5

1

4

3

-7

1

4

-3

-9

1

-11

1

-1

Integral Khovanov Homology

(db, data source)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i=-1}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i=1}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-5}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-4}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}\oplus{\mathbb Z}_2}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-3}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{4}\oplus{\mathbb Z}_2}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-2}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{4}\oplus{\mathbb Z}_2^{4}}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{4}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-1}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{4}}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{4}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=0}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{6}\oplus{\mathbb Z}_2^{5}}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{6}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=1}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{4}\oplus{\mathbb Z}_2^{5}}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{5}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=2}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{4}\oplus{\mathbb Z}_2^{4}}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{4}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=3}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}\oplus{\mathbb Z}_2^{4}}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{4}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=4}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}\oplus{\mathbb Z}_2}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=5}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}_2}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}

The Coloured Jones Polynomials

The Coloured Jones Polynomials (in the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n+1} -dimensional representation of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle sl(2)} )

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle J_n}
2	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{15}-2 q^{14}+q^{13}+5 q^{12}-11 q^{11}+2 q^{10}+21 q^9-30 q^8-5 q^7+53 q^6-48 q^5-24 q^4+85 q^3-53 q^2-44 q+99-44 q^{-1} -53 q^{-2} +85 q^{-3} -24 q^{-4} -48 q^{-5} +53 q^{-6} -5 q^{-7} -30 q^{-8} +21 q^{-9} +2 q^{-10} -11 q^{-11} +5 q^{-12} + q^{-13} -2 q^{-14} + q^{-15} }
3	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{30}+2 q^{29}-q^{28}-q^{27}-q^{26}+7 q^{25}-3 q^{24}-10 q^{23}+q^{22}+27 q^{21}-4 q^{20}-43 q^{19}-13 q^{18}+80 q^{17}+31 q^{16}-107 q^{15}-80 q^{14}+135 q^{13}+143 q^{12}-152 q^{11}-212 q^{10}+143 q^9+291 q^8-131 q^7-348 q^6+90 q^5+412 q^4-67 q^3-427 q^2+12 q+455+12 q^{-1} -427 q^{-2} -67 q^{-3} +412 q^{-4} +90 q^{-5} -348 q^{-6} -131 q^{-7} +291 q^{-8} +143 q^{-9} -212 q^{-10} -152 q^{-11} +143 q^{-12} +135 q^{-13} -80 q^{-14} -107 q^{-15} +31 q^{-16} +80 q^{-17} -13 q^{-18} -43 q^{-19} -4 q^{-20} +27 q^{-21} + q^{-22} -10 q^{-23} -3 q^{-24} +7 q^{-25} - q^{-26} - q^{-27} - q^{-28} +2 q^{-29} - q^{-30} }
4	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{50}-2 q^{49}+q^{48}+q^{47}-3 q^{46}+5 q^{45}-7 q^{44}+5 q^{43}+6 q^{42}-16 q^{41}+11 q^{40}-18 q^{39}+23 q^{38}+33 q^{37}-47 q^{36}-5 q^{35}-70 q^{34}+66 q^{33}+141 q^{32}-41 q^{31}-50 q^{30}-274 q^{29}+32 q^{28}+353 q^{27}+159 q^{26}+37 q^{25}-655 q^{24}-296 q^{23}+451 q^{22}+578 q^{21}+521 q^{20}-952 q^{19}-932 q^{18}+150 q^{17}+937 q^{16}+1362 q^{15}-873 q^{14}-1548 q^{13}-507 q^{12}+973 q^{11}+2200 q^{10}-474 q^9-1867 q^8-1182 q^7+733 q^6+2731 q^5-11 q^4-1872 q^3-1645 q^2+386 q+2903+386 q^{-1} -1645 q^{-2} -1872 q^{-3} -11 q^{-4} +2731 q^{-5} +733 q^{-6} -1182 q^{-7} -1867 q^{-8} -474 q^{-9} +2200 q^{-10} +973 q^{-11} -507 q^{-12} -1548 q^{-13} -873 q^{-14} +1362 q^{-15} +937 q^{-16} +150 q^{-17} -932 q^{-18} -952 q^{-19} +521 q^{-20} +578 q^{-21} +451 q^{-22} -296 q^{-23} -655 q^{-24} +37 q^{-25} +159 q^{-26} +353 q^{-27} +32 q^{-28} -274 q^{-29} -50 q^{-30} -41 q^{-31} +141 q^{-32} +66 q^{-33} -70 q^{-34} -5 q^{-35} -47 q^{-36} +33 q^{-37} +23 q^{-38} -18 q^{-39} +11 q^{-40} -16 q^{-41} +6 q^{-42} +5 q^{-43} -7 q^{-44} +5 q^{-45} -3 q^{-46} + q^{-47} + q^{-48} -2 q^{-49} + q^{-50} }
5	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{75}+2 q^{74}-q^{73}-q^{72}+3 q^{71}-q^{70}-5 q^{69}+5 q^{68}-4 q^{66}+10 q^{65}+3 q^{64}-19 q^{63}-2 q^{62}-q^{61}+36 q^{59}+33 q^{58}-30 q^{57}-58 q^{56}-65 q^{55}-26 q^{54}+115 q^{53}+184 q^{52}+82 q^{51}-116 q^{50}-321 q^{49}-320 q^{48}+55 q^{47}+496 q^{46}+623 q^{45}+264 q^{44}-531 q^{43}-1137 q^{42}-802 q^{41}+331 q^{40}+1510 q^{39}+1710 q^{38}+371 q^{37}-1752 q^{36}-2759 q^{35}-1527 q^{34}+1389 q^{33}+3772 q^{32}+3240 q^{31}-423 q^{30}-4456 q^{29}-5166 q^{28}-1245 q^{27}+4500 q^{26}+7083 q^{25}+3498 q^{24}-3903 q^{23}-8681 q^{22}-5933 q^{21}+2616 q^{20}+9688 q^{19}+8440 q^{18}-956 q^{17}-10187 q^{16}-10475 q^{15}-962 q^{14}+10093 q^{13}+12223 q^{12}+2709 q^{11}-9719 q^{10}-13272 q^9-4355 q^8+9034 q^7+14136 q^6+5574 q^5-8372 q^4-14366 q^3-6711 q^2+7511 q+14645+7511 q^{-1} -6711 q^{-2} -14366 q^{-3} -8372 q^{-4} +5574 q^{-5} +14136 q^{-6} +9034 q^{-7} -4355 q^{-8} -13272 q^{-9} -9719 q^{-10} +2709 q^{-11} +12223 q^{-12} +10093 q^{-13} -962 q^{-14} -10475 q^{-15} -10187 q^{-16} -956 q^{-17} +8440 q^{-18} +9688 q^{-19} +2616 q^{-20} -5933 q^{-21} -8681 q^{-22} -3903 q^{-23} +3498 q^{-24} +7083 q^{-25} +4500 q^{-26} -1245 q^{-27} -5166 q^{-28} -4456 q^{-29} -423 q^{-30} +3240 q^{-31} +3772 q^{-32} +1389 q^{-33} -1527 q^{-34} -2759 q^{-35} -1752 q^{-36} +371 q^{-37} +1710 q^{-38} +1510 q^{-39} +331 q^{-40} -802 q^{-41} -1137 q^{-42} -531 q^{-43} +264 q^{-44} +623 q^{-45} +496 q^{-46} +55 q^{-47} -320 q^{-48} -321 q^{-49} -116 q^{-50} +82 q^{-51} +184 q^{-52} +115 q^{-53} -26 q^{-54} -65 q^{-55} -58 q^{-56} -30 q^{-57} +33 q^{-58} +36 q^{-59} - q^{-61} -2 q^{-62} -19 q^{-63} +3 q^{-64} +10 q^{-65} -4 q^{-66} +5 q^{-68} -5 q^{-69} - q^{-70} +3 q^{-71} - q^{-72} - q^{-73} +2 q^{-74} - q^{-75} }
6	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{105}-2 q^{104}+q^{103}+q^{102}-3 q^{101}+q^{100}+q^{99}+7 q^{98}-10 q^{97}-2 q^{96}+9 q^{95}-11 q^{94}+2 q^{93}+7 q^{92}+28 q^{91}-24 q^{90}-25 q^{89}+15 q^{88}-34 q^{87}+35 q^{85}+112 q^{84}-13 q^{83}-74 q^{82}-26 q^{81}-167 q^{80}-88 q^{79}+64 q^{78}+381 q^{77}+228 q^{76}+32 q^{75}-53 q^{74}-602 q^{73}-662 q^{72}-338 q^{71}+671 q^{70}+970 q^{69}+1015 q^{68}+792 q^{67}-858 q^{66}-2037 q^{65}-2377 q^{64}-558 q^{63}+1092 q^{62}+3075 q^{61}+4281 q^{60}+1713 q^{59}-2051 q^{58}-5863 q^{57}-5626 q^{56}-3482 q^{55}+2486 q^{54}+9325 q^{53}+9897 q^{52}+4979 q^{51}-5026 q^{50}-12051 q^{49}-15616 q^{48}-7985 q^{47}+7805 q^{46}+19382 q^{45}+21416 q^{44}+8559 q^{43}-9501 q^{42}-28770 q^{41}-29573 q^{40}-9214 q^{39}+18063 q^{38}+38427 q^{37}+34429 q^{36}+10439 q^{35}-29717 q^{34}-51274 q^{33}-39049 q^{32}-1253 q^{31}+42472 q^{30}+59898 q^{29}+42619 q^{28}-13042 q^{27}-59892 q^{26}-67753 q^{25}-31400 q^{24}+30032 q^{23}+72651 q^{22}+72550 q^{21}+12770 q^{20}-53480 q^{19}-84155 q^{18}-58447 q^{17}+9989 q^{16}+71898 q^{15}+90602 q^{14}+35273 q^{13}-40401 q^{12}-88276 q^{11}-74856 q^{10}-7328 q^9+64968 q^8+97593 q^7+49272 q^6-28571 q^5-86374 q^4-82476 q^3-18968 q^2+57604 q+99005+57604 q^{-1} -18968 q^{-2} -82476 q^{-3} -86374 q^{-4} -28571 q^{-5} +49272 q^{-6} +97593 q^{-7} +64968 q^{-8} -7328 q^{-9} -74856 q^{-10} -88276 q^{-11} -40401 q^{-12} +35273 q^{-13} +90602 q^{-14} +71898 q^{-15} +9989 q^{-16} -58447 q^{-17} -84155 q^{-18} -53480 q^{-19} +12770 q^{-20} +72550 q^{-21} +72651 q^{-22} +30032 q^{-23} -31400 q^{-24} -67753 q^{-25} -59892 q^{-26} -13042 q^{-27} +42619 q^{-28} +59898 q^{-29} +42472 q^{-30} -1253 q^{-31} -39049 q^{-32} -51274 q^{-33} -29717 q^{-34} +10439 q^{-35} +34429 q^{-36} +38427 q^{-37} +18063 q^{-38} -9214 q^{-39} -29573 q^{-40} -28770 q^{-41} -9501 q^{-42} +8559 q^{-43} +21416 q^{-44} +19382 q^{-45} +7805 q^{-46} -7985 q^{-47} -15616 q^{-48} -12051 q^{-49} -5026 q^{-50} +4979 q^{-51} +9897 q^{-52} +9325 q^{-53} +2486 q^{-54} -3482 q^{-55} -5626 q^{-56} -5863 q^{-57} -2051 q^{-58} +1713 q^{-59} +4281 q^{-60} +3075 q^{-61} +1092 q^{-62} -558 q^{-63} -2377 q^{-64} -2037 q^{-65} -858 q^{-66} +792 q^{-67} +1015 q^{-68} +970 q^{-69} +671 q^{-70} -338 q^{-71} -662 q^{-72} -602 q^{-73} -53 q^{-74} +32 q^{-75} +228 q^{-76} +381 q^{-77} +64 q^{-78} -88 q^{-79} -167 q^{-80} -26 q^{-81} -74 q^{-82} -13 q^{-83} +112 q^{-84} +35 q^{-85} -34 q^{-87} +15 q^{-88} -25 q^{-89} -24 q^{-90} +28 q^{-91} +7 q^{-92} +2 q^{-93} -11 q^{-94} +9 q^{-95} -2 q^{-96} -10 q^{-97} +7 q^{-98} + q^{-99} + q^{-100} -3 q^{-101} + q^{-102} + q^{-103} -2 q^{-104} + q^{-105} }
7	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{140}+2 q^{139}-q^{138}-q^{137}+3 q^{136}-q^{135}-q^{134}-3 q^{133}-2 q^{132}+12 q^{131}-3 q^{130}-8 q^{129}+7 q^{128}-3 q^{127}-q^{126}-12 q^{125}-10 q^{124}+45 q^{123}+11 q^{122}-21 q^{121}-q^{120}-27 q^{119}-6 q^{118}-43 q^{117}-39 q^{116}+124 q^{115}+102 q^{114}+33 q^{113}+4 q^{112}-129 q^{111}-116 q^{110}-214 q^{109}-212 q^{108}+219 q^{107}+398 q^{106}+465 q^{105}+379 q^{104}-129 q^{103}-434 q^{102}-963 q^{101}-1195 q^{100}-334 q^{99}+576 q^{98}+1633 q^{97}+2262 q^{96}+1491 q^{95}+275 q^{94}-1996 q^{93}-4083 q^{92}-3891 q^{91}-2340 q^{90}+1273 q^{89}+5489 q^{88}+7372 q^{87}+6927 q^{86}+2127 q^{85}-5346 q^{84}-10976 q^{83}-13790 q^{82}-9783 q^{81}+675 q^{80}+12280 q^{79}+22019 q^{78}+22128 q^{77}+10764 q^{76}-7003 q^{75}-27320 q^{74}-37935 q^{73}-31183 q^{72}-8944 q^{71}+24729 q^{70}+52041 q^{69}+58145 q^{68}+38820 q^{67}-6602 q^{66}-56918 q^{65}-87316 q^{64}-81709 q^{63}-30662 q^{62}+43870 q^{61}+108006 q^{60}+131582 q^{59}+88820 q^{58}-5449 q^{57}-110563 q^{56}-178746 q^{55}-161426 q^{54}-59774 q^{53}+85085 q^{52}+209955 q^{51}+238590 q^{50}+148394 q^{49}-28036 q^{48}-215295 q^{47}-307035 q^{46}-249368 q^{45}-57689 q^{44}+188369 q^{43}+354197 q^{42}+349946 q^{41}+163581 q^{40}-130500 q^{39}-373356 q^{38}-436960 q^{37}-275780 q^{36}+48810 q^{35}+362085 q^{34}+501111 q^{33}+382490 q^{32}+45578 q^{31}-326281 q^{30}-538813 q^{29}-472292 q^{28}-140463 q^{27}+273206 q^{26}+551729 q^{25}+540897 q^{24}+226027 q^{23}-214004 q^{22}-545455 q^{21}-586355 q^{20}-296298 q^{19}+155968 q^{18}+527435 q^{17}+613307 q^{16}+349033 q^{15}-106339 q^{14}-504324 q^{13}-625272 q^{12}-386210 q^{11}+65682 q^{10}+481641 q^9+629916 q^8+411290 q^7-35563 q^6-461732 q^5-629573 q^4-429427 q^3+10614 q^2+445007 q+630069+445007 q^{-1} +10614 q^{-2} -429427 q^{-3} -629573 q^{-4} -461732 q^{-5} -35563 q^{-6} +411290 q^{-7} +629916 q^{-8} +481641 q^{-9} +65682 q^{-10} -386210 q^{-11} -625272 q^{-12} -504324 q^{-13} -106339 q^{-14} +349033 q^{-15} +613307 q^{-16} +527435 q^{-17} +155968 q^{-18} -296298 q^{-19} -586355 q^{-20} -545455 q^{-21} -214004 q^{-22} +226027 q^{-23} +540897 q^{-24} +551729 q^{-25} +273206 q^{-26} -140463 q^{-27} -472292 q^{-28} -538813 q^{-29} -326281 q^{-30} +45578 q^{-31} +382490 q^{-32} +501111 q^{-33} +362085 q^{-34} +48810 q^{-35} -275780 q^{-36} -436960 q^{-37} -373356 q^{-38} -130500 q^{-39} +163581 q^{-40} +349946 q^{-41} +354197 q^{-42} +188369 q^{-43} -57689 q^{-44} -249368 q^{-45} -307035 q^{-46} -215295 q^{-47} -28036 q^{-48} +148394 q^{-49} +238590 q^{-50} +209955 q^{-51} +85085 q^{-52} -59774 q^{-53} -161426 q^{-54} -178746 q^{-55} -110563 q^{-56} -5449 q^{-57} +88820 q^{-58} +131582 q^{-59} +108006 q^{-60} +43870 q^{-61} -30662 q^{-62} -81709 q^{-63} -87316 q^{-64} -56918 q^{-65} -6602 q^{-66} +38820 q^{-67} +58145 q^{-68} +52041 q^{-69} +24729 q^{-70} -8944 q^{-71} -31183 q^{-72} -37935 q^{-73} -27320 q^{-74} -7003 q^{-75} +10764 q^{-76} +22128 q^{-77} +22019 q^{-78} +12280 q^{-79} +675 q^{-80} -9783 q^{-81} -13790 q^{-82} -10976 q^{-83} -5346 q^{-84} +2127 q^{-85} +6927 q^{-86} +7372 q^{-87} +5489 q^{-88} +1273 q^{-89} -2340 q^{-90} -3891 q^{-91} -4083 q^{-92} -1996 q^{-93} +275 q^{-94} +1491 q^{-95} +2262 q^{-96} +1633 q^{-97} +576 q^{-98} -334 q^{-99} -1195 q^{-100} -963 q^{-101} -434 q^{-102} -129 q^{-103} +379 q^{-104} +465 q^{-105} +398 q^{-106} +219 q^{-107} -212 q^{-108} -214 q^{-109} -116 q^{-110} -129 q^{-111} +4 q^{-112} +33 q^{-113} +102 q^{-114} +124 q^{-115} -39 q^{-116} -43 q^{-117} -6 q^{-118} -27 q^{-119} - q^{-120} -21 q^{-121} +11 q^{-122} +45 q^{-123} -10 q^{-124} -12 q^{-125} - q^{-126} -3 q^{-127} +7 q^{-128} -8 q^{-129} -3 q^{-130} +12 q^{-131} -2 q^{-132} -3 q^{-133} - q^{-134} - q^{-135} +3 q^{-136} - q^{-137} - q^{-138} +2 q^{-139} - q^{-140} }

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session, or any of the Computer Talk sections above.

Modifying This Page

Read me first: Modifying Knot Pages

See/edit the Rolfsen Knot Page master template (intermediate).

See/edit the Rolfsen_Splice_Base (expert).

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10 79

Contents

Knot presentations

Three dimensional invariants

Four dimensional invariants

Polynomial invariants

"Similar" Knots (within the Atlas)

Vassiliev invariants

Khovanov Homology

The Coloured Jones Polynomials

Computer Talk

Modifying This Page

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