10 73

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10 72.gif

10_72

10 74.gif

10_74

Contents

10 73.gif
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Knot presentations

Planar diagram presentation X4251 X10,6,11,5 X8394 X2,9,3,10 X16,14,17,13 X14,7,15,8 X6,15,7,16 X20,17,1,18 X18,11,19,12 X12,19,13,20
Gauss code 1, -4, 3, -1, 2, -7, 6, -3, 4, -2, 9, -10, 5, -6, 7, -5, 8, -9, 10, -8
Dowker-Thistlethwaite code 4 8 10 14 2 18 16 6 20 12
Conway Notation [211,21,2+]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
BraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gif

Length is 12, width is 5,

Braid index is 5

10 73 ML.gif 10 73 AP.gif
[{2, 13}, {1, 6}, {12, 4}, {13, 11}, {8, 12}, {9, 7}, {6, 8}, {7, 10}, {3, 5}, {4, 9}, {5, 2}, {10, 3}, {11, 1}]

[edit Notes on presentations of 10 73]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-10][-2]
Hyperbolic Volume 13.7069
A-Polynomial See Data:10 73/A-polynomial

[edit Notes for 10 73's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 1
Topological 4 genus 1
Concordance genus 3
Rasmussen s-Invariant 2

[edit Notes for 10 73's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^3-7 t^2+20 t-27+20 t^{-1} -7 t^{-2} + t^{-3}
Conway polynomial z^6-z^4+z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 83, -2 }
Jones polynomial -q^2+4 q-7+11 q^{-1} -13 q^{-2} +14 q^{-3} -13 q^{-4} +10 q^{-5} -6 q^{-6} +3 q^{-7} - q^{-8}
HOMFLY-PT polynomial (db, data sources) -a^8+3 z^2 a^6+3 a^6-3 z^4 a^4-6 z^2 a^4-4 a^4+z^6 a^2+3 z^4 a^2+5 z^2 a^2+3 a^2-z^4-z^2
Kauffman polynomial (db, data sources) z^5 a^9-2 z^3 a^9+z a^9+3 z^6 a^8-6 z^4 a^8+4 z^2 a^8-a^8+4 z^7 a^7-5 z^5 a^7+z^3 a^7+3 z^8 a^6+3 z^6 a^6-14 z^4 a^6+12 z^2 a^6-3 a^6+z^9 a^5+10 z^7 a^5-21 z^5 a^5+14 z^3 a^5-3 z a^5+7 z^8 a^4-2 z^6 a^4-17 z^4 a^4+17 z^2 a^4-4 a^4+z^9 a^3+12 z^7 a^3-26 z^5 a^3+16 z^3 a^3-3 z a^3+4 z^8 a^2+2 z^6 a^2-16 z^4 a^2+12 z^2 a^2-3 a^2+6 z^7 a-10 z^5 a+4 z^3 a-z a+4 z^6-7 z^4+3 z^2+z^5 a^{-1} -z^3 a^{-1}
The A2 invariant -q^{26}-q^{24}+2 q^{22}+3 q^{16}-3 q^{14}-q^{10}-q^8+3 q^6-2 q^4+4 q^2- q^{-2} +2 q^{-4} - q^{-6}
The G2 invariant q^{128}-2 q^{126}+5 q^{124}-8 q^{122}+8 q^{120}-7 q^{118}-2 q^{116}+16 q^{114}-31 q^{112}+46 q^{110}-52 q^{108}+38 q^{106}-8 q^{104}-43 q^{102}+98 q^{100}-138 q^{98}+143 q^{96}-104 q^{94}+19 q^{92}+89 q^{90}-183 q^{88}+235 q^{86}-206 q^{84}+111 q^{82}+22 q^{80}-145 q^{78}+206 q^{76}-180 q^{74}+88 q^{72}+41 q^{70}-135 q^{68}+154 q^{66}-84 q^{64}-50 q^{62}+184 q^{60}-258 q^{58}+227 q^{56}-101 q^{54}-87 q^{52}+259 q^{50}-356 q^{48}+339 q^{46}-215 q^{44}+20 q^{42}+165 q^{40}-285 q^{38}+298 q^{36}-206 q^{34}+58 q^{32}+88 q^{30}-170 q^{28}+162 q^{26}-69 q^{24}-56 q^{22}+161 q^{20}-188 q^{18}+126 q^{16}+2 q^{14}-141 q^{12}+238 q^{10}-247 q^8+177 q^6-51 q^4-82 q^2+173-199 q^{-2} +165 q^{-4} -88 q^{-6} +7 q^{-8} +53 q^{-10} -83 q^{-12} +78 q^{-14} -52 q^{-16} +26 q^{-18} - q^{-20} -12 q^{-22} +14 q^{-24} -13 q^{-26} +7 q^{-28} -3 q^{-30} + q^{-32}