10 151

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10 150.gif

10_150

10 152.gif

10_152

Contents

10 151.gif
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Knot presentations

Planar diagram presentation X1425 X3849 X12,6,13,5 X9,17,10,16 X17,1,18,20 X13,19,14,18 X19,15,20,14 X15,11,16,10 X6,12,7,11 X7283
Gauss code -1, 10, -2, 1, 3, -9, -10, 2, -4, 8, 9, -3, -6, 7, -8, 4, -5, 6, -7, 5
Dowker-Thistlethwaite code 4 8 -12 2 16 -6 18 10 20 14
Conway Notation [(21,2)(21,2-)]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
BraidPart1.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gif
BraidPart2.gifBraidPart2.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gif

Length is 11, width is 4,

Braid index is 4

10 151 ML.gif 10 151 AP.gif
[{11, 5}, {1, 9}, {8, 10}, {9, 11}, {7, 4}, {5, 8}, {10, 13}, {6, 12}, {13, 7}, {12, 3}, {4, 2}, {3, 1}, {2, 6}]

[edit Notes on presentations of 10 151]


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 [-2][-8]
Hyperbolic Volume 11.843
A-Polynomial See Data:10 151/A-polynomial

[edit Notes for 10 151'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 10 151's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^3-4 t^2+10 t-13+10 t^{-1} -4 t^{-2} + t^{-3}
Conway polynomial z^6+2 z^4+3 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 43, 2 }
Jones polynomial -2 q^6+4 q^5-6 q^4+8 q^3-7 q^2+7 q-5+3 q^{-1} - q^{-2}
HOMFLY-PT polynomial (db, data sources) z^6 a^{-2} +4 z^4 a^{-2} -z^4 a^{-4} -z^4+6 z^2 a^{-2} -z^2 a^{-4} -2 z^2+3 a^{-2} - a^{-6} -1
Kauffman polynomial (db, data sources) z^8 a^{-2} +z^8 a^{-4} +3 z^7 a^{-1} +5 z^7 a^{-3} +2 z^7 a^{-5} +5 z^6 a^{-2} +3 z^6 a^{-4} +z^6 a^{-6} +3 z^6+a z^5-4 z^5 a^{-1} -7 z^5 a^{-3} -2 z^5 a^{-5} -15 z^4 a^{-2} -6 z^4 a^{-4} +2 z^4 a^{-6} -7 z^4-2 a z^3-3 z^3 a^{-1} +z^3 a^{-3} +5 z^3 a^{-5} +3 z^3 a^{-7} +10 z^2 a^{-2} +4 z^2 a^{-4} -2 z^2 a^{-6} +4 z^2+a z+2 z a^{-1} +z a^{-3} -3 z a^{-5} -3 z a^{-7} -3 a^{-2} + a^{-6} -1
The A2 invariant -q^6+q^4-q^2+2 q^{-2} - q^{-4} +3 q^{-6} +2 q^{-10} + q^{-12} - q^{-14} + q^{-16} -2 q^{-18} - q^{-20}
The G2 invariant q^{32}-2 q^{30}+5 q^{28}-8 q^{26}+7 q^{24}-4 q^{22}-6 q^{20}+19 q^{18}-30 q^{16}+34 q^{14}-27 q^{12}+q^{10}+27 q^8-52 q^6+62 q^4-46 q^2+15+23 q^{-2} -51 q^{-4} +55 q^{-6} -34 q^{-8} +33 q^{-12} -46 q^{-14} +35 q^{-16} -35 q^{-20} +62 q^{-22} -62 q^{-24} +40 q^{-26} - q^{-28} -43 q^{-30} +75 q^{-32} -80 q^{-34} +64 q^{-36} -24 q^{-38} -18 q^{-40} +56 q^{-42} -68 q^{-44} +57 q^{-46} -25 q^{-48} -11 q^{-50} +42 q^{-52} -45 q^{-54} +24 q^{-56} +13 q^{-58} -42 q^{-60} +55 q^{-62} -42 q^{-64} +5 q^{-66} +29 q^{-68} -56 q^{-70} +60 q^{-72} -45 q^{-74} +15 q^{-76} +13 q^{-78} -34 q^{-80} +34 q^{-82} -28 q^{-84} +15 q^{-86} -2 q^{-88} -7 q^{-90} +7 q^{-92} -8 q^{-94} +6 q^{-96} -2 q^{-98} + q^{-100} + q^{-102}