10 92

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10_91

10 93.gif

10_93

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Knot presentations

Planar diagram presentation X4251 X10,4,11,3 X14,6,15,5 X20,16,1,15 X16,12,17,11 X18,7,19,8 X12,18,13,17 X6,19,7,20 X8,14,9,13 X2,10,3,9
Gauss code 1, -10, 2, -1, 3, -8, 6, -9, 10, -2, 5, -7, 9, -3, 4, -5, 7, -6, 8, -4
Dowker-Thistlethwaite code 4 10 14 18 2 16 8 20 12 6
Conway Notation [.21.2.20]


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

Length is 11, width is 4,

Braid index is 4

10 92 ML.gif 10 92 AP.gif
[{3, 11}, {2, 6}, {1, 3}, {12, 8}, {10, 7}, {8, 5}, {6, 4}, {11, 9}, {5, 10}, {9, 2}, {4, 12}, {7, 1}]

[edit Notes on presentations of 10 92]


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 [1][-13]
Hyperbolic Volume 14.8554
A-Polynomial See Data:10 92/A-polynomial

[edit Notes for 10 92's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 2
Topological 4 genus 2
Concordance genus 3
Rasmussen s-Invariant -4

[edit Notes for 10 92's four dimensional invariants]

Polynomial invariants

Alexander polynomial -2 t^3+10 t^2-20 t+25-20 t^{-1} +10 t^{-2} -2 t^{-3}
Conway polynomial -2 z^6-2 z^4+2 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 89, 4 }
Jones polynomial q^{10}-4 q^9+8 q^8-12 q^7+14 q^6-15 q^5+14 q^4-10 q^3+7 q^2-3 q+1
HOMFLY-PT polynomial (db, data sources) -z^6 a^{-4} -z^6 a^{-6} +z^4 a^{-2} -2 z^4 a^{-4} -2 z^4 a^{-6} +z^4 a^{-8} +2 z^2 a^{-2} -z^2 a^{-6} +z^2 a^{-8} + a^{-2} + a^{-4} - a^{-6}
Kauffman polynomial (db, data sources) 2 z^9 a^{-5} +2 z^9 a^{-7} +4 z^8 a^{-4} +11 z^8 a^{-6} +7 z^8 a^{-8} +3 z^7 a^{-3} +5 z^7 a^{-5} +12 z^7 a^{-7} +10 z^7 a^{-9} +z^6 a^{-2} -8 z^6 a^{-4} -22 z^6 a^{-6} -5 z^6 a^{-8} +8 z^6 a^{-10} -8 z^5 a^{-3} -22 z^5 a^{-5} -32 z^5 a^{-7} -14 z^5 a^{-9} +4 z^5 a^{-11} -3 z^4 a^{-2} +2 z^4 a^{-4} +10 z^4 a^{-6} -4 z^4 a^{-8} -8 z^4 a^{-10} +z^4 a^{-12} +6 z^3 a^{-3} +18 z^3 a^{-5} +21 z^3 a^{-7} +7 z^3 a^{-9} -2 z^3 a^{-11} +3 z^2 a^{-2} +z^2 a^{-4} -2 z^2 a^{-6} +2 z^2 a^{-8} +2 z^2 a^{-10} -z a^{-3} -5 z a^{-5} -5 z a^{-7} -z a^{-9} - a^{-2} + a^{-4} + a^{-6}
The A2 invariant 1- q^{-2} + q^{-4} +2 q^{-6} -2 q^{-8} +4 q^{-10} - q^{-12} + q^{-14} + q^{-16} -3 q^{-18} +2 q^{-20} -3 q^{-22} + q^{-24} + q^{-26} -2 q^{-28} + q^{-30}
The G2 invariant  q^{-2} -2 q^{-4} +6 q^{-6} -10 q^{-8} +13 q^{-10} -12 q^{-12} +3 q^{-14} +19 q^{-16} -45 q^{-18} +75 q^{-20} -88 q^{-22} +65 q^{-24} -7 q^{-26} -85 q^{-28} +181 q^{-30} -229 q^{-32} +207 q^{-34} -97 q^{-36} -66 q^{-38} +227 q^{-40} -319 q^{-42} +300 q^{-44} -165 q^{-46} -29 q^{-48} +202 q^{-50} -276 q^{-52} +226 q^{-54} -72 q^{-56} -100 q^{-58} +223 q^{-60} -234 q^{-62} +120 q^{-64} +62 q^{-66} -250 q^{-68} +358 q^{-70} -329 q^{-72} +175 q^{-74} +56 q^{-76} -283 q^{-78} +422 q^{-80} -428 q^{-82} +287 q^{-84} -63 q^{-86} -176 q^{-88} +333 q^{-90} -352 q^{-92} +236 q^{-94} -38 q^{-96} -143 q^{-98} +230 q^{-100} -197 q^{-102} +55 q^{-104} +115 q^{-106} -235 q^{-108} +256 q^{-110} -158 q^{-112} -6 q^{-114} +173 q^{-116} -275 q^{-118} +278 q^{-120} -193 q^{-122} +61 q^{-124} +66 q^{-126} -157 q^{-128} +184 q^{-130} -156 q^{-132} +99 q^{-134} -28 q^{-136} -26 q^{-138} +54 q^{-140} -65 q^{-142} +54 q^{-144} -34 q^{-146} +16 q^{-148} + q^{-150} -8 q^{-152} +10 q^{-154} -10 q^{-156} +6 q^{-158} -3 q^{-160} + q^{-162}