9 26

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9 25.gif

9_25

9 27.gif

9_27

Contents

9 26.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 X7,15,8,14 X17,7,18,6 X9,17,10,16 X15,9,16,8
Gauss code -1, 4, -3, 1, -2, 7, -6, 9, -8, 3, -4, 2, -5, 6, -9, 8, -7, 5
Dowker-Thistlethwaite code 4 10 12 14 16 2 18 8 6
Conway Notation [311112]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
BraidPart1.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart2.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 9, width is 4,

Braid index is 4

9 26 ML.gif 9 26 AP.gif
[{11, 4}, {3, 9}, {10, 5}, {4, 6}, {9, 11}, {5, 2}, {8, 3}, {6, 1}, {7, 10}, {2, 8}, {1, 7}]

[edit Notes on presentations of 9 26]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 3
Bridge index 2
Super bridge index \{4,6\}
Nakanishi index 1
Maximal Thurston-Bennequin number [-2][-9]
Hyperbolic Volume 10.5958
A-Polynomial See Data:9 26/A-polynomial

[edit Notes for 9 26's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 1
Topological 4 genus 1
Concordance genus 3
Rasmussen s-Invariant 2

[edit Notes for 9 26's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^3-5 t^2+11 t-13+11 t^{-1} -5 t^{-2} + t^{-3}
Conway polynomial z^6+z^4+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 47, 2 }
Jones polynomial q^7-3 q^6+5 q^5-7 q^4+8 q^3-8 q^2+7 q-4+3 q^{-1} - q^{-2}
HOMFLY-PT polynomial (db, data sources) z^6 a^{-2} +4 z^4 a^{-2} -2 z^4 a^{-4} -z^4+6 z^2 a^{-2} -5 z^2 a^{-4} +z^2 a^{-6} -2 z^2+3 a^{-2} -3 a^{-4} + a^{-6}
Kauffman polynomial (db, data sources) z^8 a^{-2} +z^8 a^{-4} +3 z^7 a^{-1} +6 z^7 a^{-3} +3 z^7 a^{-5} +5 z^6 a^{-2} +6 z^6 a^{-4} +4 z^6 a^{-6} +3 z^6+a z^5-6 z^5 a^{-1} -11 z^5 a^{-3} -z^5 a^{-5} +3 z^5 a^{-7} -16 z^4 a^{-2} -14 z^4 a^{-4} -5 z^4 a^{-6} +z^4 a^{-8} -8 z^4-2 a z^3+3 z^3 a^{-1} +7 z^3 a^{-3} -2 z^3 a^{-5} -4 z^3 a^{-7} +13 z^2 a^{-2} +11 z^2 a^{-4} +2 z^2 a^{-6} -z^2 a^{-8} +5 z^2-z a^{-1} -z a^{-3} +z a^{-5} +z a^{-7} -3 a^{-2} -3 a^{-4} - a^{-6}
The A2 invariant -q^6+q^4+1+3 q^{-2} - q^{-4} +2 q^{-6} - q^{-8} -2 q^{-14} + q^{-16} - q^{-18} + q^{-22}
The G2 invariant q^{32}-2 q^{30}+4 q^{28}-7 q^{26}+5 q^{24}-4 q^{22}-4 q^{20}+16 q^{18}-23 q^{16}+28 q^{14}-23 q^{12}+8 q^{10}+15 q^8-39 q^6+53 q^4-49 q^2+30+2 q^{-2} -31 q^{-4} +51 q^{-6} -49 q^{-8} +35 q^{-10} -5 q^{-12} -23 q^{-14} +35 q^{-16} -28 q^{-18} +6 q^{-20} +25 q^{-22} -40 q^{-24} +44 q^{-26} -23 q^{-28} -10 q^{-30} +46 q^{-32} -73 q^{-34} +76 q^{-36} -53 q^{-38} +12 q^{-40} +33 q^{-42} -67 q^{-44} +78 q^{-46} -62 q^{-48} +28 q^{-50} +5 q^{-52} -38 q^{-54} +44 q^{-56} -31 q^{-58} +4 q^{-60} +21 q^{-62} -33 q^{-64} +26 q^{-66} -4 q^{-68} -25 q^{-70} +44 q^{-72} -50 q^{-74} +40 q^{-76} -15 q^{-78} -15 q^{-80} +38 q^{-82} -46 q^{-84} +44 q^{-86} -27 q^{-88} +9 q^{-90} +8 q^{-92} -21 q^{-94} +24 q^{-96} -19 q^{-98} +13 q^{-100} -4 q^{-102} -2 q^{-104} +4 q^{-106} -6 q^{-108} +4 q^{-110} -2 q^{-112} + q^{-114}