10 94

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10 93.gif

10_93

10 95.gif

10_95

Contents

10 94.gif
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Knot presentations

Planar diagram presentation X6271 X2837 X18,12,19,11 X14,5,15,6 X20,14,1,13 X8,15,9,16 X10,4,11,3 X16,9,17,10 X4,17,5,18 X12,20,13,19
Gauss code 1, -2, 7, -9, 4, -1, 2, -6, 8, -7, 3, -10, 5, -4, 6, -8, 9, -3, 10, -5
Dowker-Thistlethwaite code 6 10 14 2 16 18 20 8 4 12
Conway Notation [.30.2.2]


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

Length is 10, width is 3,

Braid index is 3

10 94 ML.gif 10 94 AP.gif
[{7, 12}, {2, 11}, {12, 8}, {6, 1}, {5, 7}, {4, 6}, {3, 5}, {9, 4}, {8, 2}, {10, 3}, {11, 9}, {1, 10}]

[edit Notes on presentations of 10 94]


Three dimensional invariants

Symmetry type Chiral
Unknotting number 2
3-genus 4
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-3][-9]
Hyperbolic Volume 13.3116
A-Polynomial See Data:10 94/A-polynomial

[edit Notes for 10 94's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for 10 94's four dimensional invariants]

Polynomial invariants

Alexander polynomial -t^4+4 t^3-9 t^2+14 t-15+14 t^{-1} -9 t^{-2} +4 t^{-3} - t^{-4}
Conway polynomial -z^8-4 z^6-5 z^4-2 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 71, 2 }
Jones polynomial q^7-3 q^6+6 q^5-9 q^4+11 q^3-12 q^2+11 q-8+6 q^{-1} -3 q^{-2} + q^{-3}
HOMFLY-PT polynomial (db, data sources) -z^8 a^{-2} -6 z^6 a^{-2} +z^6 a^{-4} +z^6-13 z^4 a^{-2} +4 z^4 a^{-4} +4 z^4-12 z^2 a^{-2} +5 z^2 a^{-4} +5 z^2-4 a^{-2} +2 a^{-4} +3
Kauffman polynomial (db, data sources) 2 z^9 a^{-1} +2 z^9 a^{-3} +9 z^8 a^{-2} +5 z^8 a^{-4} +4 z^8+3 a z^7+3 z^7 a^{-3} +6 z^7 a^{-5} +a^2 z^6-27 z^6 a^{-2} -9 z^6 a^{-4} +5 z^6 a^{-6} -12 z^6-9 a z^5-11 z^5 a^{-1} -15 z^5 a^{-3} -10 z^5 a^{-5} +3 z^5 a^{-7} -3 a^2 z^4+31 z^4 a^{-2} +10 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} +11 z^4+6 a z^3+10 z^3 a^{-1} +16 z^3 a^{-3} +9 z^3 a^{-5} -3 z^3 a^{-7} +2 a^2 z^2-18 z^2 a^{-2} -6 z^2 a^{-4} +2 z^2 a^{-6} -z^2 a^{-8} -7 z^2-a z-3 z a^{-1} -5 z a^{-3} -3 z a^{-5} +4 a^{-2} +2 a^{-4} +3
The A2 invariant q^8-q^6+2 q^4+1+2 q^{-2} -3 q^{-4} +2 q^{-6} -3 q^{-8} + q^{-10} - q^{-14} +2 q^{-16} - q^{-18} + q^{-20}
The G2 invariant q^{46}-2 q^{44}+5 q^{42}-9 q^{40}+10 q^{38}-9 q^{36}+17 q^{32}-34 q^{30}+51 q^{28}-55 q^{26}+35 q^{24}+5 q^{22}-60 q^{20}+111 q^{18}-124 q^{16}+97 q^{14}-28 q^{12}-55 q^{10}+125 q^8-149 q^6+116 q^4-36 q^2-49+109 q^{-2} -110 q^{-4} +59 q^{-6} +24 q^{-8} -87 q^{-10} +112 q^{-12} -89 q^{-14} +15 q^{-16} +69 q^{-18} -141 q^{-20} +167 q^{-22} -135 q^{-24} +54 q^{-26} +49 q^{-28} -143 q^{-30} +185 q^{-32} -173 q^{-34} +99 q^{-36} -95 q^{-40} +144 q^{-42} -127 q^{-44} +62 q^{-46} +25 q^{-48} -86 q^{-50} +94 q^{-52} -53 q^{-54} -19 q^{-56} +84 q^{-58} -110 q^{-60} +97 q^{-62} -39 q^{-64} -29 q^{-66} +84 q^{-68} -109 q^{-70} +99 q^{-72} -63 q^{-74} +18 q^{-76} +23 q^{-78} -53 q^{-80} +65 q^{-82} -58 q^{-84} +44 q^{-86} -20 q^{-88} -2 q^{-90} +17 q^{-92} -28 q^{-94} +26 q^{-96} -19 q^{-98} +11 q^{-100} -2 q^{-102} -3 q^{-104} +5 q^{-106} -6 q^{-108} +4 q^{-110} -2 q^{-112} + q^{-114}