9 2

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9 1.gif

9_1

9 3.gif

9_3

Contents

9 2.gif
(KnotPlot image)

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Knot presentations

Planar diagram presentation X1425 X3,12,4,13 X5,18,6,1 X7,16,8,17 X9,14,10,15 X13,10,14,11 X15,8,16,9 X17,6,18,7 X11,2,12,3
Gauss code -1, 9, -2, 1, -3, 8, -4, 7, -5, 6, -9, 2, -6, 5, -7, 4, -8, 3
Dowker-Thistlethwaite code 4 12 18 16 14 2 10 8 6
Conway Notation [72]


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

Length is 12, width is 5,

Braid index is 5

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

[edit Notes on presentations of 9 2]

Knot 9_2.
A graph, knot 9_2.

Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 1
Bridge index 2
Super bridge index \{4,7\}
Nakanishi index 1
Maximal Thurston-Bennequin number [-12][1]
Hyperbolic Volume 3.48666
A-Polynomial See Data:9 2/A-polynomial

[edit Notes for 9 2's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for 9 2's four dimensional invariants]

Polynomial invariants

Alexander polynomial 4 t-7+4 t^{-1}
Conway polynomial 4 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 15, -2 }
Jones polynomial  q^{-1} - q^{-2} +2 q^{-3} -2 q^{-4} +2 q^{-5} -2 q^{-6} +2 q^{-7} - q^{-8} + q^{-9} - q^{-10}
HOMFLY-PT polynomial (db, data sources) -a^{10}+z^2 a^8+a^8+z^2 a^6+z^2 a^4+z^2 a^2+a^2
Kauffman polynomial (db, data sources) z^7 a^{11}-6 z^5 a^{11}+10 z^3 a^{11}-4 z a^{11}+z^8 a^{10}-6 z^6 a^{10}+11 z^4 a^{10}-7 z^2 a^{10}+a^{10}+2 z^7 a^9-10 z^5 a^9+13 z^3 a^9-4 z a^9+z^8 a^8-5 z^6 a^8+8 z^4 a^8-6 z^2 a^8+a^8+z^7 a^7-3 z^5 a^7+z^3 a^7+z^6 a^6-2 z^4 a^6+z^5 a^5-z^3 a^5+z^4 a^4+z^3 a^3+z^2 a^2-a^2
The A2 invariant -q^{32}-q^{30}+q^{24}+q^{22}+q^8+q^6+q^2
The G2 invariant q^{156}+q^{152}-q^{150}+q^{142}-2 q^{140}+q^{138}-q^{136}-q^{134}-2 q^{130}-q^{128}-q^{126}-q^{124}-q^{118}+q^{112}-q^{108}+q^{106}+q^{104}+2 q^{102}+q^{98}+q^{94}+q^{92}-2 q^{90}+q^{88}+q^{86}+q^{76}-q^{72}+q^{66}-q^{62}-q^{52}+q^{48}+q^{38}+q^{34}+q^{28}+q^{24}+q^{20}+q^{14}+q^{10}