10 154

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10 153.gif

10_153

10 155.gif

10_155

Contents

10 154.gif
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Knot presentations

Planar diagram presentation X4251 X8493 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 X2837
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.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart2.gifBraidPart1.gifBraidPart1.gifBraidPart1.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart2.gifBraidPart2.gifBraidPart2.gifBraidPart1.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gif

Length is 11, width is 4,

Braid index is 4

10 154 ML.gif 10 154 AP.gif
[{3, 10}, {2, 4}, {1, 3}, {11, 9}, {10, 2}, {5, 8}, {9, 7}, {8, 6}, {7, 12}, {4, 11}, {12, 5}, {6, 1}]

[edit Notes on presentations of 10 154]

Knot 10_154.
A graph, knot 10_154.
A part of a knot and a part of a graph.

Three dimensional invariants

Symmetry type Reversible
Unknotting number 3
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [5][-15]
Hyperbolic Volume 9.24989
A-Polynomial See Data:10 154/A-polynomial

[edit Notes for 10 154's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 3
Topological 4 genus [2,3]
Concordance genus 3
Rasmussen s-Invariant -6

[edit Notes for 10 154's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^3-4 t+7-4 t^{-1} + t^{-3}
Conway polynomial z^6+6 z^4+5 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 13, 4 }
Jones polynomial q^{12}-2 q^{11}+2 q^{10}-3 q^9+2 q^8-2 q^7+2 q^6+q^3
HOMFLY-PT polynomial (db, data sources) z^6 a^{-6} +6 z^4 a^{-6} +9 z^2 a^{-6} -2 z^2 a^{-8} -2 z^2 a^{-10} +4 a^{-6} -2 a^{-8} -2 a^{-10} + a^{-12}
Kauffman polynomial (db, data sources) z^8 a^{-10} +z^8 a^{-12} +z^7 a^{-9} +3 z^7 a^{-11} +2 z^7 a^{-13} +z^6 a^{-6} -5 z^6 a^{-10} -3 z^6 a^{-12} +z^6 a^{-14} -6 z^5 a^{-9} -15 z^5 a^{-11} -9 z^5 a^{-13} -6 z^4 a^{-6} -2 z^4 a^{-8} +7 z^4 a^{-10} -z^4 a^{-12} -4 z^4 a^{-14} -2 z^3 a^{-7} +9 z^3 a^{-9} +21 z^3 a^{-11} +10 z^3 a^{-13} +9 z^2 a^{-6} +5 z^2 a^{-8} -5 z^2 a^{-10} +2 z^2 a^{-12} +3 z^2 a^{-14} +3 z a^{-7} -3 z a^{-9} -10 z a^{-11} -4 z a^{-13} -4 a^{-6} -2 a^{-8} +2 a^{-10} + a^{-12}
The A2 invariant  q^{-10} + q^{-12} + q^{-14} +2 q^{-16} +2 q^{-18} + q^{-22} - q^{-24} - q^{-26} -2 q^{-28} -2 q^{-30} - q^{-34} + q^{-36} + q^{-38}
The G2 invariant  q^{-50} + q^{-52} +2 q^{-56} + q^{-58} +3 q^{-62} + q^{-66} +3 q^{-68} -2 q^{-70} +3 q^{-72} +3 q^{-74} -4 q^{-76} +7 q^{-78} -5 q^{-80} +2 q^{-82} +5 q^{-84} -7 q^{-86} +9 q^{-88} -4 q^{-90} -4 q^{-92} +8 q^{-94} -5 q^{-96} +7 q^{-100} -10 q^{-102} +8 q^{-104} -2 q^{-106} -6 q^{-108} +8 q^{-110} -9 q^{-112} +6 q^{-114} -5 q^{-116} -2 q^{-118} + q^{-120} -3 q^{-122} -6 q^{-126} -2 q^{-130} -2 q^{-132} + q^{-134} -4 q^{-136} -2 q^{-138} +8 q^{-140} -10 q^{-142} +6 q^{-144} -7 q^{-148} +14 q^{-150} -10 q^{-152} +6 q^{-154} +4 q^{-156} -5 q^{-158} +8 q^{-160} -3 q^{-162} - q^{-164} +6 q^{-166} -4 q^{-168} +3 q^{-172} -5 q^{-174} +6 q^{-176} -4 q^{-178} - q^{-180} + q^{-182} -3 q^{-184} +2 q^{-186} - q^{-188} + q^{-190}