10 145

From Knot Atlas
Jump to: navigation, search

10 144.gif

10_144

10 146.gif

10_146

Contents

10 145.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

Visit 10 145's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit 10 145 at Knotilus!


Knot presentations

Planar diagram presentation X4251 X5,12,6,13 X8394 X2,9,3,10 X11,16,12,17 X17,10,18,11 X7,18,8,19 X13,20,14,1 X19,14,20,15 X15,6,16,7
Gauss code 1, -4, 3, -1, -2, 10, -7, -3, 4, 6, -5, 2, -8, 9, -10, 5, -6, 7, -9, 8
Dowker-Thistlethwaite code 4 8 -12 -18 2 -16 -20 -6 -10 -14
Conway Notation [22,3,3-]


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

Length is 11, width is 4,

Braid index is 4

10 145 ML.gif 10 145 AP.gif
[{4, 11}, {10, 3}, {1, 5}, {2, 4}, {3, 9}, {8, 10}, {9, 6}, {11, 7}, {5, 8}, {6, 2}, {7, 1}]

[edit Notes on presentations of 10 145]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 2
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-12][3]
Hyperbolic Volume 5.0449
A-Polynomial See Data:10 145/A-polynomial

[edit Notes for 10 145's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 2
Topological 4 genus [1,2]
Concordance genus 2
Rasmussen s-Invariant 4

[edit Notes for 10 145's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^2+t-3+ t^{-1} + t^{-2}
Conway polynomial z^4+5 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 3, -2 }
Jones polynomial  q^{-2} + q^{-7} - q^{-8} + q^{-9} - q^{-10}
HOMFLY-PT polynomial (db, data sources) -a^{10}+z^2 a^8+a^8-a^6+z^4 a^4+4 z^2 a^4+2 a^4
Kauffman polynomial (db, data sources) z^7 a^{11}-6 z^5 a^{11}+10 z^3 a^{11}-5 z a^{11}+z^8 a^{10}-6 z^6 a^{10}+10 z^4 a^{10}-6 z^2 a^{10}+a^{10}+2 z^7 a^9-12 z^5 a^9+18 z^3 a^9-6 z a^9+z^8 a^8-6 z^6 a^8+9 z^4 a^8-4 z^2 a^8+a^8+z^7 a^7-6 z^5 a^7+8 z^3 a^7-2 z a^7-2 z^2 a^6+a^6-z a^5+z^4 a^4-4 z^2 a^4+2 a^4
The A2 invariant -q^{32}-q^{30}+q^{24}+q^{14}+q^{10}+q^8+q^6
The G2 invariant q^{156}+q^{152}-q^{148}+q^{142}-2 q^{138}-q^{130}-3 q^{128}-q^{126}+q^{124}-q^{122}-q^{120}-q^{118}-2 q^{116}+2 q^{114}-2 q^{112}-q^{110}+q^{108}+2 q^{104}+2 q^{102}+q^{98}+q^{96}+2 q^{92}+q^{88}+2 q^{82}-q^{78}-3 q^{76}+q^{74}-q^{72}-3 q^{66}+2 q^{64}+q^{62}-2 q^{60}-q^{54}+3 q^{52}+2 q^{48}+q^{46}+3 q^{42}+q^{38}+q^{32}+q^{30}