9 43

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9 42.gif

9_42

9 44.gif

9_44

Contents

9 43.gif
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Knot presentations

Planar diagram presentation X4251 X10,6,11,5 X8394 X2,9,3,10 X14,8,15,7 X15,1,16,18 X11,17,12,16 X17,13,18,12 X6,14,7,13
Gauss code 1, -4, 3, -1, 2, -9, 5, -3, 4, -2, -7, 8, 9, -5, -6, 7, -8, 6
Dowker-Thistlethwaite code 4 8 10 14 2 -16 6 -18 -12
Conway Notation [211,3,2-]


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

Length is 9, width is 4,

Braid index is 4

9 43 ML.gif 9 43 AP.gif
[{5, 10}, {9, 1}, {10, 8}, {6, 9}, {4, 7}, {3, 6}, {2, 5}, {1, 4}, {7, 2}, {8, 3}]

[edit Notes on presentations of 9 43]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 3
Bridge index 3
Super bridge index \{4,5\}
Nakanishi index 1
Maximal Thurston-Bennequin number [1][-10]
Hyperbolic Volume 5.90409
A-Polynomial See Data:9 43/A-polynomial

[edit Notes for 9 43's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for 9 43's four dimensional invariants]

Polynomial invariants

Alexander polynomial -t^3+3 t^2-2 t+1-2 t^{-1} +3 t^{-2} - t^{-3}
Conway polynomial -z^6-3 z^4+z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 13, 4 }
Jones polynomial -q^7+2 q^6-2 q^5+2 q^4-2 q^3+2 q^2-q+1
HOMFLY-PT polynomial (db, data sources) -z^6 a^{-4} +z^4 a^{-2} -5 z^4 a^{-4} +z^4 a^{-6} +4 z^2 a^{-2} -7 z^2 a^{-4} +4 z^2 a^{-6} +3 a^{-2} -4 a^{-4} +3 a^{-6} - a^{-8}
Kauffman polynomial (db, data sources) z^7 a^{-3} +z^7 a^{-5} +z^6 a^{-2} +3 z^6 a^{-4} +2 z^6 a^{-6} -4 z^5 a^{-3} -3 z^5 a^{-5} +z^5 a^{-7} -5 z^4 a^{-2} -13 z^4 a^{-4} -8 z^4 a^{-6} +3 z^3 a^{-3} +z^3 a^{-5} -2 z^3 a^{-7} +7 z^2 a^{-2} +14 z^2 a^{-4} +9 z^2 a^{-6} +2 z^2 a^{-8} +z a^{-7} +z a^{-9} -3 a^{-2} -4 a^{-4} -3 a^{-6} - a^{-8}
The A2 invariant 1+ q^{-2} + q^{-4} + q^{-6} -2 q^{-12} + q^{-18} + q^{-20} - q^{-26}
The G2 invariant  q^{-2} +2 q^{-6} - q^{-8} + q^{-10} + q^{-12} - q^{-14} +4 q^{-16} - q^{-18} +2 q^{-20} + q^{-22} - q^{-24} +3 q^{-26} - q^{-30} +2 q^{-32} - q^{-34} +2 q^{-38} -3 q^{-40} +2 q^{-42} -2 q^{-44} - q^{-48} -3 q^{-50} + q^{-52} -3 q^{-54} + q^{-56} -2 q^{-58} - q^{-64} + q^{-66} - q^{-68} +2 q^{-72} +3 q^{-78} -2 q^{-80} +4 q^{-82} +2 q^{-88} -2 q^{-90} +2 q^{-92} - q^{-100} - q^{-102} + q^{-104} - q^{-106} - q^{-108} - q^{-112} - q^{-116} + q^{-120}