9 14

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9 13.gif

9_13

9 15.gif

9_15

Contents

9 14.gif
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Knot presentations

Planar diagram presentation X1425 X5,12,6,13 X3,11,4,10 X11,3,12,2 X13,18,14,1 X9,15,10,14 X7,17,8,16 X15,9,16,8 X17,7,18,6
Gauss code -1, 4, -3, 1, -2, 9, -7, 8, -6, 3, -4, 2, -5, 6, -8, 7, -9, 5
Dowker-Thistlethwaite code 4 10 12 16 14 2 18 8 6
Conway Notation [41112]


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

Length is 10, width is 5,

Braid index is 5

9 14 ML.gif 9 14 AP.gif
[{11, 3}, {2, 9}, {10, 4}, {3, 5}, {9, 11}, {4, 1}, {6, 2}, {5, 7}, {8, 6}, {7, 10}, {1, 8}]

[edit Notes on presentations of 9 14]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 2
Bridge index 2
Super bridge index \{4,7\}
Nakanishi index 1
Maximal Thurston-Bennequin number [-4][-7]
Hyperbolic Volume 8.95499
A-Polynomial See Data:9 14/A-polynomial

[edit Notes for 9 14'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 9 14's four dimensional invariants]

Polynomial invariants

Alexander polynomial 2 t^2-9 t+15-9 t^{-1} +2 t^{-2}
Conway polynomial 2 z^4-z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 37, 0 }
Jones polynomial q^6-2 q^5+3 q^4-5 q^3+6 q^2-6 q+6-4 q^{-1} +3 q^{-2} - q^{-3}
HOMFLY-PT polynomial (db, data sources) z^4 a^{-2} +z^4-a^2 z^2+z^2 a^{-2} -2 z^2 a^{-4} +z^2+ a^{-2} -2 a^{-4} + a^{-6} +1
Kauffman polynomial (db, data sources) z^8 a^{-2} +z^8 a^{-4} +3 z^7 a^{-1} +5 z^7 a^{-3} +2 z^7 a^{-5} +3 z^6 a^{-2} +z^6 a^{-6} +4 z^6+4 a z^5-4 z^5 a^{-1} -16 z^5 a^{-3} -8 z^5 a^{-5} +3 a^2 z^4-12 z^4 a^{-2} -9 z^4 a^{-4} -4 z^4 a^{-6} -4 z^4+a^3 z^3-3 a z^3+2 z^3 a^{-1} +15 z^3 a^{-3} +9 z^3 a^{-5} -2 a^2 z^2+8 z^2 a^{-2} +10 z^2 a^{-4} +4 z^2 a^{-6} -2 z a^{-1} -5 z a^{-3} -3 z a^{-5} - a^{-2} -2 a^{-4} - a^{-6} +1
The A2 invariant -q^{10}+q^8+q^6-q^4+2 q^2+ q^{-2} + q^{-4} + q^{-8} -2 q^{-10} - q^{-12} - q^{-16} + q^{-18} + q^{-20}
The G2 invariant q^{52}-2 q^{50}+3 q^{48}-4 q^{46}+q^{44}-3 q^{40}+8 q^{38}-10 q^{36}+11 q^{34}-8 q^{32}+2 q^{30}+4 q^{28}-10 q^{26}+16 q^{24}-16 q^{22}+14 q^{20}-8 q^{18}-q^{16}+11 q^{14}-15 q^{12}+17 q^{10}-12 q^8+3 q^6+6 q^4-10 q^2+10-2 q^{-2} -6 q^{-4} +15 q^{-6} -16 q^{-8} +9 q^{-10} +5 q^{-12} -19 q^{-14} +30 q^{-16} -28 q^{-18} +18 q^{-20} -16 q^{-24} +28 q^{-26} -30 q^{-28} +23 q^{-30} -10 q^{-32} -6 q^{-34} +16 q^{-36} -19 q^{-38} +15 q^{-40} -5 q^{-42} -7 q^{-44} +11 q^{-46} -13 q^{-48} +5 q^{-50} +5 q^{-52} -16 q^{-54} +21 q^{-56} -19 q^{-58} +6 q^{-60} +8 q^{-62} -20 q^{-64} +25 q^{-66} -21 q^{-68} +11 q^{-70} + q^{-72} -10 q^{-74} +16 q^{-76} -14 q^{-78} +10 q^{-80} -2 q^{-82} -2 q^{-84} +3 q^{-86} -4 q^{-88} +3 q^{-90} - q^{-92} + q^{-94}