10 148

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10 147.gif

10_147

10 149.gif

10_149

Contents

10 148.gif
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Knot presentations

Planar diagram presentation X4251 X8493 X5,12,6,13 X13,18,14,19 X9,16,10,17 X17,10,18,11 X15,20,16,1 X19,14,20,15 X11,6,12,7 X2837
Gauss code 1, -10, 2, -1, -3, 9, 10, -2, -5, 6, -9, 3, -4, 8, -7, 5, -6, 4, -8, 7
Dowker-Thistlethwaite code 4 8 -12 2 -16 -6 -18 -20 -10 -14
Conway Notation [(3,2)(3,2-)]


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

Length is 10, width is 3,

Braid index is 3

10 148 ML.gif 10 148 AP.gif
[{3, 5}, {2, 4}, {1, 3}, {13, 6}, {5, 12}, {10, 13}, {11, 7}, {6, 8}, {4, 10}, {7, 9}, {8, 11}, {12, 2}, {9, 1}]

[edit Notes on presentations of 10 148]


Three dimensional invariants

Symmetry type Chiral
Unknotting number 2
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-10][0]
Hyperbolic Volume 10.2602
A-Polynomial See Data:10 148/A-polynomial

[edit Notes for 10 148'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 10 148's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^3-3 t^2+7 t-9+7 t^{-1} -3 t^{-2} + t^{-3}
Conway polynomial z^6+3 z^4+4 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 31, -2 }
Jones polynomial -1+3 q^{-1} -4 q^{-2} +6 q^{-3} -5 q^{-4} +5 q^{-5} -4 q^{-6} +2 q^{-7} - q^{-8}
HOMFLY-PT polynomial (db, data sources) -z^4 a^6-3 z^2 a^6-3 a^6+z^6 a^4+5 z^4 a^4+9 z^2 a^4+5 a^4-z^4 a^2-2 z^2 a^2-a^2
Kauffman polynomial (db, data sources) z^5 a^9-3 z^3 a^9+2 z a^9+2 z^6 a^8-5 z^4 a^8+2 z^2 a^8+2 z^7 a^7-4 z^5 a^7+z^3 a^7-z a^7+z^8 a^6-z^6 a^6+2 z^4 a^6-6 z^2 a^6+3 a^6+3 z^7 a^5-7 z^5 a^5+9 z^3 a^5-5 z a^5+z^8 a^4-3 z^6 a^4+10 z^4 a^4-11 z^2 a^4+5 a^4+z^7 a^3-2 z^5 a^3+6 z^3 a^3-3 z a^3+3 z^4 a^2-3 z^2 a^2+a^2+z^3 a-z a
The A2 invariant -q^{24}-2 q^{20}-q^{18}+q^{16}+3 q^{12}+q^{10}+2 q^8+q^6-q^4+q^2-1
The G2 invariant q^{128}-q^{126}+3 q^{124}-4 q^{122}+3 q^{120}-q^{118}-3 q^{116}+9 q^{114}-13 q^{112}+15 q^{110}-11 q^{108}-q^{106}+12 q^{104}-22 q^{102}+25 q^{100}-18 q^{98}+3 q^{96}+10 q^{94}-23 q^{92}+20 q^{90}-11 q^{88}-7 q^{86}+17 q^{84}-21 q^{82}+10 q^{80}+5 q^{78}-21 q^{76}+28 q^{74}-25 q^{72}+12 q^{70}+4 q^{68}-20 q^{66}+31 q^{64}-29 q^{62}+22 q^{60}-5 q^{58}-8 q^{56}+22 q^{54}-24 q^{52}+20 q^{50}-5 q^{48}-6 q^{46}+19 q^{44}-16 q^{42}+7 q^{40}+12 q^{38}-21 q^{36}+25 q^{34}-14 q^{32}-2 q^{30}+17 q^{28}-24 q^{26}+24 q^{24}-13 q^{22}+2 q^{20}+7 q^{18}-13 q^{16}+10 q^{14}-7 q^{12}+3 q^{10}-2 q^6-q^2+1- q^{-2} + q^{-4}