10 133

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10 132.gif

10_132

10 134.gif

10_134

Contents

10 133.gif
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Knot presentations

Planar diagram presentation X1425 X3849 X14,9,15,10 X5,13,6,12 X13,7,14,6 X18,11,19,12 X20,15,1,16 X16,19,17,20 X10,17,11,18 X7283
Gauss code -1, 10, -2, 1, -4, 5, -10, 2, 3, -9, 6, 4, -5, -3, 7, -8, 9, -6, 8, -7
Dowker-Thistlethwaite code 4 8 12 2 -14 -18 6 -20 -10 -16
Conway Notation [23,21,2-]


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

10 133 ML.gif 10 133 AP.gif
[{9, 1}, {11, 7}, {6, 8}, {7, 9}, {4, 10}, {1, 6}, {5, 3}, {8, 4}, {2, 5}, {3, 11}, {10, 2}]

[edit Notes on presentations of 10 133]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 2
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-11][1]
Hyperbolic Volume 7.7983
A-Polynomial See Data:10 133/A-polynomial

[edit Notes for 10 133'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 10 133's four dimensional invariants]

Polynomial invariants

Alexander polynomial -t^2+5 t-7+5 t^{-1} - t^{-2}
Conway polynomial -z^4+z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 19, -2 }
Jones polynomial  q^{-1} - q^{-2} +3 q^{-3} -3 q^{-4} +3 q^{-5} -3 q^{-6} +2 q^{-7} -2 q^{-8} + q^{-9}
HOMFLY-PT polynomial (db, data sources) z^2 a^8+a^8-z^4 a^6-3 z^2 a^6-3 a^6+2 z^2 a^4+2 a^4+z^2 a^2+a^2
Kauffman polynomial (db, data sources) z^6 a^{10}-4 z^4 a^{10}+3 z^2 a^{10}+2 z^7 a^9-9 z^5 a^9+10 z^3 a^9-3 z a^9+z^8 a^8-3 z^6 a^8+z^2 a^8+a^8+3 z^7 a^7-13 z^5 a^7+16 z^3 a^7-7 z a^7+z^8 a^6-4 z^6 a^6+6 z^4 a^6-6 z^2 a^6+3 a^6+z^7 a^5-4 z^5 a^5+7 z^3 a^5-4 z a^5+2 z^4 a^4-3 z^2 a^4+2 a^4+z^3 a^3+z^2 a^2-a^2
The A2 invariant q^{28}-2 q^{20}-q^{18}-q^{16}+q^{12}+q^{10}+2 q^8+q^6+q^2
The G2 invariant q^{142}-q^{140}+2 q^{138}-3 q^{136}+q^{134}-q^{132}-3 q^{130}+6 q^{128}-6 q^{126}+4 q^{124}-q^{122}-2 q^{120}+5 q^{118}-4 q^{116}+2 q^{114}+3 q^{112}-3 q^{110}+4 q^{108}+q^{106}-3 q^{104}+8 q^{102}-6 q^{100}+3 q^{98}+q^{96}-4 q^{94}+5 q^{92}-6 q^{90}+3 q^{88}-4 q^{86}-q^{82}-5 q^{80}+q^{78}-4 q^{76}-3 q^{70}+q^{66}-4 q^{64}+6 q^{62}-5 q^{60}+2 q^{58}+4 q^{56}-5 q^{54}+7 q^{52}-2 q^{50}+q^{48}+3 q^{46}-2 q^{44}+q^{42}+2 q^{40}+2 q^{36}+q^{34}-q^{32}+2 q^{30}-q^{28}+q^{26}+q^{24}-q^{22}+2 q^{20}+q^{14}+q^{10}