10 143

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10 142.gif

10_142

10 144.gif

10_144

Contents

10 143.gif
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Knot presentations

Planar diagram presentation X4251 X10,4,11,3 X5,14,6,15 X7,16,8,17 X15,6,16,7 X17,20,18,1 X11,18,12,19 X19,12,20,13 X13,8,14,9 X2,10,3,9
Gauss code 1, -10, 2, -1, -3, 5, -4, 9, 10, -2, -7, 8, -9, 3, -5, 4, -6, 7, -8, 6
Dowker-Thistlethwaite code 4 10 -14 -16 2 -18 -8 -6 -20 -12
Conway Notation [31,3,21-]


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

Length is 10, width is 3,

Braid index is 3

10 143 ML.gif 10 143 AP.gif
[{3, 8}, {2, 4}, {1, 3}, {13, 9}, {8, 10}, {9, 11}, {10, 12}, {11, 5}, {4, 6}, {5, 7}, {6, 13}, {12, 2}, {7, 1}]

[edit Notes on presentations of 10 143]


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][0]
Hyperbolic Volume 9.0709
A-Polynomial See Data:10 143/A-polynomial

[edit Notes for 10 143's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for 10 143's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^3-3 t^2+6 t-7+6 t^{-1} -3 t^{-2} + t^{-3}
Conway polynomial z^6+3 z^4+3 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 27, -2 }
Jones polynomial -1+3 q^{-1} -3 q^{-2} +5 q^{-3} -5 q^{-4} +4 q^{-5} -3 q^{-6} +2 q^{-7} - q^{-8}
HOMFLY-PT polynomial (db, data sources) -z^4 a^6-3 z^2 a^6-2 a^6+z^6 a^4+5 z^4 a^4+8 z^2 a^4+3 a^4-z^4 a^2-2 z^2 a^2
Kauffman polynomial (db, data sources) z^5 a^9-3 z^3 a^9+z a^9+2 z^6 a^8-6 z^4 a^8+3 z^2 a^8+2 z^7 a^7-6 z^5 a^7+5 z^3 a^7-2 z a^7+z^8 a^6-2 z^6 a^6+2 z^4 a^6-3 z^2 a^6+2 a^6+3 z^7 a^5-10 z^5 a^5+14 z^3 a^5-5 z a^5+z^8 a^4-4 z^6 a^4+11 z^4 a^4-10 z^2 a^4+3 a^4+z^7 a^3-3 z^5 a^3+7 z^3 a^3-3 z a^3+3 z^4 a^2-4 z^2 a^2+z^3 a-z a
The A2 invariant -q^{24}-q^{20}+q^{16}-q^{14}+q^{12}+2 q^8+2 q^6+q^2-1
The G2 invariant q^{128}-q^{126}+2 q^{124}-3 q^{122}+2 q^{120}-q^{118}-2 q^{116}+7 q^{114}-8 q^{112}+9 q^{110}-7 q^{108}+5 q^{104}-13 q^{102}+15 q^{100}-11 q^{98}+2 q^{96}+6 q^{94}-11 q^{92}+11 q^{90}-6 q^{88}-4 q^{86}+8 q^{84}-13 q^{82}+7 q^{80}+2 q^{78}-12 q^{76}+18 q^{74}-14 q^{72}+8 q^{70}+2 q^{68}-11 q^{66}+14 q^{64}-19 q^{62}+15 q^{60}-3 q^{58}-4 q^{56}+10 q^{54}-14 q^{52}+14 q^{50}-q^{48}-5 q^{46}+5 q^{44}-9 q^{42}+9 q^{40}+8 q^{38}-13 q^{36}+14 q^{34}-7 q^{32}+3 q^{30}+10 q^{28}-16 q^{26}+11 q^{24}-6 q^{22}+5 q^{20}+2 q^{18}-8 q^{16}+7 q^{14}-3 q^{12}+3 q^{10}-q^8-q^6-q^4-q^2+1- q^{-2} + q^{-4}