9 7

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9 6.gif

9_6

9 8.gif

9_8

Contents

9 7.gif
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Knot presentations

Planar diagram presentation X1425 X3,12,4,13 X5,16,6,17 X7,18,8,1 X17,6,18,7 X9,14,10,15 X13,10,14,11 X15,8,16,9 X11,2,12,3
Gauss code -1, 9, -2, 1, -3, 5, -4, 8, -6, 7, -9, 2, -7, 6, -8, 3, -5, 4
Dowker-Thistlethwaite code 4 12 16 18 14 2 10 8 6
Conway Notation [342]


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

Length is 11, width is 4,

Braid index is 4

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

[edit Notes on presentations of 9 7]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 2
Bridge index 2
Super bridge index \{4,6\}
Nakanishi index 1
Maximal Thurston-Bennequin number [-14][3]
Hyperbolic Volume 8.01486
A-Polynomial See Data:9 7/A-polynomial

[edit Notes for 9 7's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for 9 7's four dimensional invariants]

Polynomial invariants

Alexander polynomial 3 t^2-7 t+9-7 t^{-1} +3 t^{-2}
Conway polynomial 3 z^4+5 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 29, -4 }
Jones polynomial  q^{-2} - q^{-3} +3 q^{-4} -4 q^{-5} +5 q^{-6} -5 q^{-7} +4 q^{-8} -3 q^{-9} +2 q^{-10} - q^{-11}
HOMFLY-PT polynomial (db, data sources) -z^2 a^{10}-a^{10}+z^4 a^8+2 z^2 a^8+a^8+z^4 a^6+z^2 a^6-a^6+z^4 a^4+3 z^2 a^4+2 a^4
Kauffman polynomial (db, data sources) z^5 a^{13}-3 z^3 a^{13}+z a^{13}+2 z^6 a^{12}-6 z^4 a^{12}+3 z^2 a^{12}+2 z^7 a^{11}-6 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+z^8 a^{10}-2 z^6 a^{10}+2 z^4 a^{10}-2 z^2 a^{10}+a^{10}+3 z^7 a^9-9 z^5 a^9+11 z^3 a^9-3 z a^9+z^8 a^8-3 z^6 a^8+7 z^4 a^8-4 z^2 a^8+a^8+z^7 a^7-z^5 a^7+2 z^3 a^7-z a^7+z^6 a^6-2 z^2 a^6+a^6+z^5 a^5-z^3 a^5-z a^5+z^4 a^4-3 z^2 a^4+2 a^4
The A2 invariant -q^{34}-q^{28}+q^{26}-q^{18}+q^{16}+q^{12}+2 q^{10}+q^6
The G2 invariant q^{176}-q^{174}+2 q^{172}-3 q^{170}+2 q^{168}-q^{166}-2 q^{164}+7 q^{162}-8 q^{160}+9 q^{158}-7 q^{156}+6 q^{152}-12 q^{150}+13 q^{148}-11 q^{146}+4 q^{144}+4 q^{142}-10 q^{140}+10 q^{138}-6 q^{136}+5 q^{132}-9 q^{130}+5 q^{128}-7 q^{124}+11 q^{122}-12 q^{120}+8 q^{118}-q^{116}-8 q^{114}+13 q^{112}-16 q^{110}+15 q^{108}-7 q^{106}-q^{104}+9 q^{102}-13 q^{100}+14 q^{98}-7 q^{96}+q^{94}+5 q^{92}-7 q^{90}+5 q^{88}+q^{86}-6 q^{84}+8 q^{82}-7 q^{80}+4 q^{76}-9 q^{74}+10 q^{72}-8 q^{70}+4 q^{68}-q^{66}-4 q^{64}+6 q^{62}-6 q^{60}+7 q^{58}-3 q^{56}+3 q^{54}+q^{52}-q^{50}+4 q^{48}-3 q^{46}+4 q^{44}-q^{42}+q^{40}+q^{38}-q^{36}+2 q^{34}+q^{30}