10 35

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10 34.gif

10_34

10 36.gif

10_36

Contents

10 35.gif
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Knot presentations

Planar diagram presentation X1425 X7,10,8,11 X3948 X9,3,10,2 X5,16,6,17 X11,1,12,20 X13,19,14,18 X17,15,18,14 X19,13,20,12 X15,6,16,7
Gauss code -1, 4, -3, 1, -5, 10, -2, 3, -4, 2, -6, 9, -7, 8, -10, 5, -8, 7, -9, 6
Dowker-Thistlethwaite code 4 8 16 10 2 20 18 6 14 12
Conway Notation [2422]


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.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gif

Length is 11, width is 6,

Braid index is 6

10 35 ML.gif 10 35 AP.gif
[{12, 9}, {10, 8}, {9, 11}, {5, 10}, {7, 1}, {8, 6}, {2, 7}, {6, 12}, {1, 3}, {4, 2}, {3, 5}, {11, 4}]

[edit Notes on presentations of 10 35]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 2
Bridge index 2
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-5][-7]
Hyperbolic Volume 10.3945
A-Polynomial See Data:10 35/A-polynomial

[edit Notes for 10 35'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 35's four dimensional invariants]

Polynomial invariants

Alexander polynomial 2 t^2-12 t+21-12 t^{-1} +2 t^{-2}
Conway polynomial 2 z^4-4 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 49, 0 }
Jones polynomial q^6-2 q^5+4 q^4-6 q^3+7 q^2-8 q+8-6 q^{-1} +4 q^{-2} -2 q^{-3} + q^{-4}
HOMFLY-PT polynomial (db, data sources) a^4-2 z^2 a^2-a^2+z^4+1+z^4 a^{-2} -2 z^2 a^{-4} - a^{-4} + a^{-6}
Kauffman polynomial (db, data sources) z^9 a^{-1} +z^9 a^{-3} +4 z^8 a^{-2} +2 z^8 a^{-4} +2 z^8+2 a z^7+2 z^7 a^{-5} +2 a^2 z^6-11 z^6 a^{-2} -5 z^6 a^{-4} +z^6 a^{-6} -3 z^6+2 a^3 z^5-z^5 a^{-1} -6 z^5 a^{-3} -7 z^5 a^{-5} +a^4 z^4+10 z^4 a^{-2} -4 z^4 a^{-6} +5 z^4-3 a^3 z^3-2 a z^3+5 z^3 a^{-3} +6 z^3 a^{-5} -2 a^4 z^2-3 a^2 z^2-3 z^2 a^{-2} +3 z^2 a^{-4} +4 z^2 a^{-6} -3 z^2+a^3 z+a z+z a^{-1} -z a^{-3} -2 z a^{-5} +a^4+a^2- a^{-4} - a^{-6} +1
The A2 invariant q^{14}+q^{12}-q^{10}+q^8-2 q^4+2 q^2+ q^{-2} - q^{-6} + q^{-8} -2 q^{-10} + q^{-14} - q^{-16} + q^{-18} + q^{-20}
The G2 invariant Data:10 35/QuantumInvariant/G2/1,0