9 45

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9 44.gif

9_44

9 46.gif

9_46

Contents

9 45.gif
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Knot presentations

Planar diagram presentation X4251 X10,6,11,5 X8394 X2,9,3,10 X7,14,8,15 X18,15,1,16 X16,11,17,12 X12,17,13,18 X13,6,14,7
Gauss code 1, -4, 3, -1, 2, 9, -5, -3, 4, -2, 7, -8, -9, 5, 6, -7, 8, -6
Dowker-Thistlethwaite code 4 8 10 -14 2 16 -6 18 12
Conway Notation [211,21,2-]


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

Length is 9, width is 4,

Braid index is 4

9 45 ML.gif 9 45 AP.gif
[{2, 11}, {1, 7}, {10, 4}, {11, 9}, {6, 8}, {7, 10}, {3, 5}, {4, 6}, {5, 2}, {8, 3}, {9, 1}]

[edit Notes on presentations of 9 45]

Knot 9_45.
A graph, knot 9_45.
A part of a knot and a part of a graph.

Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 2
Bridge index 3
Super bridge index \{4,5\}
Nakanishi index 1
Maximal Thurston-Bennequin number [-10][1]
Hyperbolic Volume 8.60203
A-Polynomial See Data:9 45/A-polynomial

[edit Notes for 9 45's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for 9 45's four dimensional invariants]

Polynomial invariants

Alexander polynomial -t^2+6 t-9+6 t^{-1} - t^{-2}
Conway polynomial -z^4+2 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 23, -2 }
Jones polynomial 2 q^{-1} -3 q^{-2} +4 q^{-3} -4 q^{-4} +4 q^{-5} -3 q^{-6} +2 q^{-7} - q^{-8}
HOMFLY-PT polynomial (db, data sources) -a^8+2 z^2 a^6+2 a^6-z^4 a^4-2 z^2 a^4-2 a^4+2 z^2 a^2+2 a^2
Kauffman polynomial (db, data sources) z^5 a^9-3 z^3 a^9+2 z a^9+2 z^6 a^8-6 z^4 a^8+4 z^2 a^8-a^8+z^7 a^7-5 z^3 a^7+2 z a^7+4 z^6 a^6-10 z^4 a^6+7 z^2 a^6-2 a^6+z^7 a^5-z^3 a^5+2 z^6 a^4-4 z^4 a^4+6 z^2 a^4-2 a^4+z^5 a^3+z^3 a^3+3 z^2 a^2-2 a^2
The A2 invariant -q^{26}-q^{24}+q^{22}+q^{18}+q^{16}-q^{14}-q^{10}+q^8+q^6+2 q^2
The G2 invariant q^{128}-q^{126}+3 q^{124}-4 q^{122}+2 q^{120}-5 q^{116}+9 q^{114}-10 q^{112}+8 q^{110}-3 q^{108}-7 q^{106}+10 q^{104}-12 q^{102}+8 q^{100}-3 q^{98}-6 q^{96}+9 q^{94}-7 q^{92}+2 q^{90}+6 q^{88}-9 q^{86}+10 q^{84}-4 q^{82}-2 q^{80}+9 q^{78}-12 q^{76}+15 q^{74}-9 q^{72}+3 q^{70}+7 q^{68}-12 q^{66}+14 q^{64}-12 q^{62}+5 q^{60}+2 q^{58}-9 q^{56}+9 q^{54}-8 q^{52}+q^{50}+6 q^{48}-10 q^{46}+6 q^{44}-q^{42}-7 q^{40}+11 q^{38}-11 q^{36}+8 q^{34}-5 q^{30}+9 q^{28}-8 q^{26}+8 q^{24}-q^{22}-q^{20}+2 q^{18}-2 q^{16}+3 q^{14}-q^{12}+2 q^{10}+q^8