10 3

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10 2.gif

10_2

10 4.gif

10_4

Contents

10 3.gif
(KnotPlot image)

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Knot presentations

Planar diagram presentation X1627 X11,16,12,17 X5,13,6,12 X3,15,4,14 X13,5,14,4 X15,3,16,2 X7,20,8,1 X9,18,10,19 X17,10,18,11 X19,8,20,9
Gauss code -1, 6, -4, 5, -3, 1, -7, 10, -8, 9, -2, 3, -5, 4, -6, 2, -9, 8, -10, 7
Dowker-Thistlethwaite code 6 14 12 20 18 16 4 2 10 8
Conway Notation [64]


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

Length is 13, width is 6,

Braid index is 6

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

[edit Notes on presentations of 10 3]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 1
Bridge index 2
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-7][-5]
Hyperbolic Volume 5.7321
A-Polynomial See Data:10 3/A-polynomial

[edit Notes for 10 3'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 3's four dimensional invariants]

Polynomial invariants

Alexander polynomial -6 t+13-6 t^{-1}
Conway polynomial 1-6 z^2
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 25, 0 }
Jones polynomial q^4-q^3+2 q^2-3 q+4-4 q^{-1} +3 q^{-2} -3 q^{-3} +2 q^{-4} - q^{-5} + q^{-6}
HOMFLY-PT polynomial (db, data sources) a^6-z^2 a^4-2 z^2 a^2-a^2-2 z^2-z^2 a^{-2} + a^{-4}
Kauffman polynomial (db, data sources) a^3 z^9+a z^9+a^4 z^8+2 a^2 z^8+z^8+a^5 z^7-6 a^3 z^7-6 a z^7+z^7 a^{-1} +a^6 z^6-4 a^4 z^6-10 a^2 z^6+z^6 a^{-2} -4 z^6-4 a^5 z^5+15 a^3 z^5+15 a z^5-3 z^5 a^{-1} +z^5 a^{-3} -5 a^6 z^4+4 a^4 z^4+18 a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} +6 z^4+3 a^5 z^3-18 a^3 z^3-15 a z^3+4 z^3 a^{-1} -2 z^3 a^{-3} +6 a^6 z^2-2 a^4 z^2-12 a^2 z^2+z^2 a^{-2} -3 z^2 a^{-4} +6 a^3 z+6 a z-a^6+a^2+ a^{-4}
The A2 invariant q^{20}+q^{18}+q^{14}-q^{10}-q^6-q^4+ q^{-2} - q^{-4} + q^{-8} + q^{-12} + q^{-14}
The G2 invariant Data:10 3/QuantumInvariant/G2/1,0