10 135

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10 134.gif

10_134

10 136.gif

10_136

Contents

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Knot presentations

Planar diagram presentation X1425 X3849 X9,15,10,14 X12,5,13,6 X6,13,7,14 X11,19,12,18 X15,1,16,20 X19,17,20,16 X17,11,18,10 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 [221,21,2-]


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

Length is 11, width is 4,

Braid index is 4

10 135 ML.gif 10 135 AP.gif
[{6, 8}, {7, 9}, {8, 12}, {11, 6}, {1, 10}, {9, 11}, {5, 2}, {4, 1}, {3, 5}, {12, 4}, {2, 7}, {10, 3}]

[edit Notes on presentations of 10 135]


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 [-6][-4]
Hyperbolic Volume 10.6872
A-Polynomial See Data:10 135/A-polynomial

[edit Notes for 10 135's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 1
Topological 4 genus 1
Concordance genus 2
Rasmussen s-Invariant 0

[edit Notes for 10 135's four dimensional invariants]

Polynomial invariants

Alexander polynomial 3 t^2-9 t+13-9 t^{-1} +3 t^{-2}
Conway polynomial 3 z^4+3 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 37, 0 }
Jones polynomial -2 q^3+4 q^2-5 q+7-6 q^{-1} +6 q^{-2} -4 q^{-3} +2 q^{-4} - q^{-5}
HOMFLY-PT polynomial (db, data sources) -z^2 a^4-a^4+z^4 a^2+z^2 a^2+2 z^4+5 z^2+4-2 z^2 a^{-2} -2 a^{-2}
Kauffman polynomial (db, data sources) a^2 z^8+z^8+2 a^3 z^7+4 a z^7+2 z^7 a^{-1} +2 a^4 z^6+a^2 z^6+z^6 a^{-2} +a^5 z^5-3 a^3 z^5-8 a z^5-4 z^5 a^{-1} -5 a^4 z^4-4 a^2 z^4+2 z^4 a^{-2} +3 z^4-3 a^5 z^3-a^3 z^3+8 a z^3+9 z^3 a^{-1} +3 z^3 a^{-3} +3 a^4 z^2+a^2 z^2-4 z^2 a^{-2} -6 z^2+2 a^5 z+a^3 z-4 a z-6 z a^{-1} -3 z a^{-3} -a^4+2 a^{-2} +4
The A2 invariant -q^{16}-2 q^{10}+q^8+q^4+3 q^2+1+3 q^{-2} - q^{-4} -2 q^{-10}
The G2 invariant q^{80}-q^{78}+3 q^{76}-4 q^{74}+3 q^{72}-2 q^{70}-3 q^{68}+9 q^{66}-15 q^{64}+17 q^{62}-15 q^{60}+3 q^{58}+9 q^{56}-25 q^{54}+35 q^{52}-32 q^{50}+17 q^{48}+3 q^{46}-25 q^{44}+35 q^{42}-31 q^{40}+14 q^{38}+7 q^{36}-24 q^{34}+26 q^{32}-14 q^{30}-9 q^{28}+30 q^{26}-37 q^{24}+31 q^{22}-10 q^{20}-18 q^{18}+42 q^{16}-50 q^{14}+46 q^{12}-24 q^{10}-q^8+30 q^6-41 q^4+45 q^2-27+8 q^{-2} +18 q^{-4} -27 q^{-6} +25 q^{-8} -6 q^{-10} -12 q^{-12} +30 q^{-14} -29 q^{-16} +14 q^{-18} +7 q^{-20} -29 q^{-22} +39 q^{-24} -37 q^{-26} +19 q^{-28} -20 q^{-32} +26 q^{-34} -26 q^{-36} +16 q^{-38} -5 q^{-40} -4 q^{-42} +5 q^{-44} -9 q^{-46} +6 q^{-48} -2 q^{-50} + q^{-52} + q^{-54}