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10 138

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10 137.gif

10_137

10 139.gif

10_139

Contents

10 138.gif
(KnotPlot image)

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Knot presentations

Planar diagram presentation X4251 X10,6,11,5 X8394 X2,9,3,10 X16,12,17,11 X7,15,8,14 X15,7,16,6 X20,18,1,17 X18,13,19,14 X12,19,13,20
Gauss code 1, -4, 3, -1, 2, 7, -6, -3, 4, -2, 5, -10, 9, 6, -7, -5, 8, -9, 10, -8
Dowker-Thistlethwaite code 4 8 10 -14 2 16 18 -6 20 12
Conway Notation [211,211,2-]


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

Length is 10, width is 5,

Braid index is 5

10 138 ML.gif 10 138 AP.gif
[{2, 11}, {1, 7}, {10, 6}, {11, 9}, {8, 3}, {7, 10}, {5, 2}, {6, 4}, {3, 5}, {4, 8}, {9, 1}]

[edit Notes on presentations of 10 138]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-3][-7]
Hyperbolic Volume 10.4672
A-Polynomial See Data:10 138/A-polynomial

[edit Notes for 10 138's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 1
Topological 4 genus 1
Concordance genus 3
Rasmussen s-Invariant -2

[edit Notes for 10 138's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^3-5 t^2+8 t-7+8 t^{-1} -5 t^{-2} + t^{-3}
Conway polynomial z^6+z^4-3 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 35, 2 }
Jones polynomial 2 q^5-4 q^4+5 q^3-6 q^2+6 q-5+4 q^{-1} -2 q^{-2} + q^{-3}
HOMFLY-PT polynomial (db, data sources) z^6 a^{-2} +4 z^4 a^{-2} -z^4 a^{-4} -2 z^4+a^2 z^2+5 z^2 a^{-2} -3 z^2 a^{-4} -6 z^2+2 a^2+3 a^{-2} -2 a^{-4} + a^{-6} -3
Kauffman polynomial (db, data sources) z^8 a^{-2} +z^8+2 a z^7+5 z^7 a^{-1} +3 z^7 a^{-3} +a^2 z^6+3 z^6 a^{-2} +3 z^6 a^{-4} +z^6-7 a z^5-14 z^5 a^{-1} -6 z^5 a^{-3} +z^5 a^{-5} -4 a^2 z^4-13 z^4 a^{-2} -5 z^4 a^{-4} -12 z^4+6 a z^3+8 z^3 a^{-1} +5 z^3 a^{-3} +3 z^3 a^{-5} +5 a^2 z^2+10 z^2 a^{-2} +6 z^2 a^{-4} +3 z^2 a^{-6} +12 z^2-a z-z a^{-1} -2 z a^{-3} -2 z a^{-5} -2 a^2-3 a^{-2} -2 a^{-4} - a^{-6} -3
The A2 invariant q^{10}+q^8+q^4-q^2- q^{-4} +2 q^{-6} - q^{-8} + q^{-10} - q^{-12} - q^{-14} + q^{-16} + q^{-20}
The G2 invariant q^{46}-q^{44}+4 q^{42}-5 q^{40}+5 q^{38}-2 q^{36}-4 q^{34}+14 q^{32}-18 q^{30}+20 q^{28}-11 q^{26}-4 q^{24}+19 q^{22}-27 q^{20}+29 q^{18}-16 q^{16}+17 q^{12}-25 q^{10}+19 q^8-5 q^6-13 q^4+20 q^2-21+7 q^{-2} +8 q^{-4} -25 q^{-6} +33 q^{-8} -29 q^{-10} +14 q^{-12} +5 q^{-14} -25 q^{-16} +35 q^{-18} -34 q^{-20} +24 q^{-22} -4 q^{-24} -12 q^{-26} +28 q^{-28} -27 q^{-30} +17 q^{-32} + q^{-34} -15 q^{-36} +22 q^{-38} -17 q^{-40} +16 q^{-44} -24 q^{-46} +25 q^{-48} -15 q^{-50} -5 q^{-52} +18 q^{-54} -26 q^{-56} +22 q^{-58} -13 q^{-60} + q^{-62} +9 q^{-64} -12 q^{-66} +11 q^{-68} -8 q^{-70} +5 q^{-72} + q^{-74} -3 q^{-76} + q^{-78} -2 q^{-80} +2 q^{-82} - q^{-84} +2 q^{-86} + q^{-88}