10 129

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10 128.gif

10_128

10 130.gif

10_130

Contents

10 129.gif
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Knot presentations

Planar diagram presentation X1425 X3849 X5,14,6,15 X20,16,1,15 X16,10,17,9 X10,20,11,19 X18,12,19,11 X12,18,13,17 X13,6,14,7 X7283
Gauss code -1, 10, -2, 1, -3, 9, -10, 2, 5, -6, 7, -8, -9, 3, 4, -5, 8, -7, 6, -4
Dowker-Thistlethwaite code 4 8 14 2 -16 -18 6 -20 -12 -10
Conway Notation [32,21,2-]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
BraidPart1.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart2.gifBraidPart2.gifBraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gif

Length is 11, width is 4,

Braid index is 4

10 129 ML.gif 10 129 AP.gif
[{12, 2}, {1, 10}, {8, 11}, {10, 12}, {9, 3}, {2, 8}, {5, 1}, {4, 6}, {7, 5}, {6, 9}, {3, 7}, {11, 4}]

[edit Notes on presentations of 10 129]


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 [-6][-4]
Hyperbolic Volume 8.90152
A-Polynomial See Data:10 129/A-polynomial

[edit Notes for 10 129's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 0
Topological 4 genus 0
Concordance genus 0
Rasmussen s-Invariant 0

[edit Notes for 10 129's four dimensional invariants]

Polynomial invariants

Alexander polynomial 2 t^2-6 t+9-6 t^{-1} +2 t^{-2}
Conway polynomial 2 z^4+2 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 25, 0 }
Jones polynomial -q^3+2 q^2-3 q+5-4 q^{-1} +4 q^{-2} -3 q^{-3} +2 q^{-4} - q^{-5}
HOMFLY-PT polynomial (db, data sources) -z^2 a^4-a^4+z^4 a^2+2 z^2 a^2+a^2+z^4+2 z^2+2-z^2 a^{-2} - a^{-2}
Kauffman polynomial (db, data sources) a^2 z^8+z^8+2 a^3 z^7+3 a z^7+z^7 a^{-1} +2 a^4 z^6-2 a^2 z^6-4 z^6+a^5 z^5-6 a^3 z^5-11 a z^5-4 z^5 a^{-1} -6 a^4 z^4+2 z^4 a^{-2} +8 z^4-3 a^5 z^3+4 a^3 z^3+15 a z^3+9 z^3 a^{-1} +z^3 a^{-3} +3 a^4 z^2+2 a^2 z^2-3 z^2 a^{-2} -4 z^2+a^5 z-a^3 z-5 a z-5 z a^{-1} -2 z a^{-3} -a^4-a^2+ a^{-2} +2
The A2 invariant -q^{16}-q^{10}+q^8+q^4+2 q^2+1+2 q^{-2} - q^{-4} - q^{-10}
The G2 invariant q^{80}-q^{78}+2 q^{76}-3 q^{74}+2 q^{72}-q^{70}-3 q^{68}+6 q^{66}-8 q^{64}+8 q^{62}-7 q^{60}-q^{58}+6 q^{56}-11 q^{54}+12 q^{52}-7 q^{50}+6 q^{46}-9 q^{44}+7 q^{42}-q^{40}-7 q^{38}+11 q^{36}-10 q^{34}+4 q^{32}+6 q^{30}-13 q^{28}+16 q^{26}-12 q^{24}+5 q^{22}+2 q^{20}-10 q^{18}+14 q^{16}-12 q^{14}+9 q^{12}-3 q^8+10 q^6-8 q^4+6 q^2+2-4 q^{-2} +10 q^{-4} -6 q^{-6} + q^{-8} +10 q^{-10} -12 q^{-12} +13 q^{-14} -7 q^{-16} -4 q^{-18} +8 q^{-20} -11 q^{-22} +9 q^{-24} -5 q^{-26} - q^{-28} +3 q^{-30} -5 q^{-32} +2 q^{-34} - q^{-36} - q^{-38} - q^{-44} + q^{-52}