10 153

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10 152.gif

10_152

10 154.gif

10_154

Contents

10 153.gif
(KnotPlot image)

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10_153 is not k-colourable for any k. See The Determinant and the Signature.

Knot presentations

Planar diagram presentation X4251 X8493 X12,6,13,5 X13,18,14,19 X9,16,10,17 X17,10,18,11 X15,20,16,1 X19,14,20,15 X6,12,7,11 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)-(21,2)]


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

Length is 11, width is 4,

Braid index is 4

10 153 ML.gif 10 153 AP.gif
[{3, 9}, {2, 4}, {1, 3}, {10, 5}, {9, 2}, {11, 6}, {5, 7}, {4, 10}, {6, 8}, {7, 11}, {8, 1}]

[edit Notes on presentations of 10 153]

Knot 10_153.
A graph, knot 10_153.
A part of a knot and a part of a graph.

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 [-6][-4]
Hyperbolic Volume 7.37434
A-Polynomial See Data:10 153/A-polynomial

[edit Notes for 10 153's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 0
Topological 4 genus 0
Concordance genus 0
Rasmussen s-Invariant 0

[edit Notes for 10 153's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^3-t^2-t+3- t^{-1} - t^{-2} + t^{-3}
Conway polynomial z^6+5 z^4+4 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 1, 0 }
Jones polynomial -q^4+q^3-q^2+q+1+ q^{-2} - q^{-3} + q^{-4} - q^{-5}
HOMFLY-PT polynomial (db, data sources) z^6-z^4 a^{-2} +6 z^4-a^4 z^2-a^2 z^2-4 z^2 a^{-2} +10 z^2-a^4-a^2-3 a^{-2} +6
Kauffman polynomial (db, data sources) z^8 a^{-2} +z^8+a z^7+2 z^7 a^{-1} +z^7 a^{-3} +a^4 z^6-6 z^6 a^{-2} -7 z^6+a^5 z^5+a^3 z^5-7 a z^5-13 z^5 a^{-1} -6 z^5 a^{-3} -4 a^4 z^4+10 z^4 a^{-2} +14 z^4-4 a^5 z^3-4 a^3 z^3+12 a z^3+22 z^3 a^{-1} +10 z^3 a^{-3} +3 a^4 z^2-2 a^2 z^2-7 z^2 a^{-2} -12 z^2+3 a^5 z+2 a^3 z-6 a z-10 z a^{-1} -5 z a^{-3} -a^4+a^2+3 a^{-2} +6
The A2 invariant -q^{16}-q^{12}-q^{10}+2 q^4+2 q^2+3+2 q^{-2} - q^{-8} - q^{-10} - q^{-12}
The G2 invariant q^{80}+q^{76}-q^{74}+q^{70}-2 q^{68}+q^{64}-3 q^{62}+q^{60}-q^{58}-4 q^{56}+5 q^{54}-5 q^{52}+q^{50}+q^{48}-5 q^{46}+5 q^{44}-3 q^{42}-2 q^{40}+2 q^{38}-4 q^{36}+q^{34}+3 q^{32}-5 q^{30}+3 q^{28}-q^{24}+2 q^{22}-2 q^{20}+2 q^{18}+4 q^{14}-2 q^{12}+3 q^{10}+4 q^8-q^6+5 q^4-q^2+2+6 q^{-2} - q^{-4} +2 q^{-6} +4 q^{-8} -2 q^{-10} +6 q^{-12} - q^{-14} -3 q^{-16} +4 q^{-18} -4 q^{-20} +2 q^{-22} -3 q^{-26} + q^{-28} - q^{-30} -3 q^{-32} -2 q^{-36} - q^{-38} -3 q^{-42} - q^{-48} - q^{-52} + q^{-56} + q^{-60}