9 32

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9 31.gif

9_31

9 33.gif

9_33

Contents

9 32.gif
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Knot presentations

Planar diagram presentation X1425 X13,18,14,1 X3948 X9,3,10,2 X7,15,8,14 X15,11,16,10 X5,12,6,13 X11,17,12,16 X17,7,18,6
Gauss code -1, 4, -3, 1, -7, 9, -5, 3, -4, 6, -8, 7, -2, 5, -6, 8, -9, 2
Dowker-Thistlethwaite code 4 8 12 14 2 16 18 10 6
Conway Notation [.21.20]


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

Length is 9, width is 4,

Braid index is 4

9 32 ML.gif 9 32 AP.gif
[{11, 8}, {3, 9}, {7, 2}, {8, 4}, {6, 3}, {4, 1}, {5, 7}, {2, 6}, {10, 5}, {9, 11}, {1, 10}]

[edit Notes on presentations of 9 32]


Three dimensional invariants

Symmetry type Chiral
Unknotting number 2
3-genus 3
Bridge index 3
Super bridge index \{4,6\}
Nakanishi index 1
Maximal Thurston-Bennequin number [-2][-9]
Hyperbolic Volume 13.0999
A-Polynomial See Data:9 32/A-polynomial

[edit Notes for 9 32'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 32's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^3-6 t^2+14 t-17+14 t^{-1} -6 t^{-2} + t^{-3}
Conway polynomial z^6-z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 59, 2 }
Jones polynomial q^7-3 q^6+6 q^5-9 q^4+10 q^3-10 q^2+9 q-6+4 q^{-1} - q^{-2}
HOMFLY-PT polynomial (db, data sources) z^6 a^{-2} +3 z^4 a^{-2} -2 z^4 a^{-4} -z^4+3 z^2 a^{-2} -4 z^2 a^{-4} +z^2 a^{-6} -z^2+ a^{-2} -2 a^{-4} + a^{-6} +1
Kauffman polynomial (db, data sources) 2 z^8 a^{-2} +2 z^8 a^{-4} +5 z^7 a^{-1} +10 z^7 a^{-3} +5 z^7 a^{-5} +6 z^6 a^{-2} +7 z^6 a^{-4} +5 z^6 a^{-6} +4 z^6+a z^5-9 z^5 a^{-1} -18 z^5 a^{-3} -5 z^5 a^{-5} +3 z^5 a^{-7} -19 z^4 a^{-2} -18 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} -8 z^4-a z^3+3 z^3 a^{-1} +9 z^3 a^{-3} +2 z^3 a^{-5} -3 z^3 a^{-7} +10 z^2 a^{-2} +12 z^2 a^{-4} +4 z^2 a^{-6} -z^2 a^{-8} +3 z^2-z a^{-1} -2 z a^{-3} +z a^{-7} - a^{-2} -2 a^{-4} - a^{-6} +1
The A2 invariant -q^6+2 q^4+1+3 q^{-2} -2 q^{-4} +2 q^{-6} -2 q^{-8} -2 q^{-14} +2 q^{-16} - q^{-18} + q^{-22}
The G2 invariant q^{32}-3 q^{30}+7 q^{28}-13 q^{26}+13 q^{24}-9 q^{22}-6 q^{20}+30 q^{18}-50 q^{16}+66 q^{14}-56 q^{12}+17 q^{10}+39 q^8-93 q^6+126 q^4-112 q^2+58+22 q^{-2} -92 q^{-4} +126 q^{-6} -106 q^{-8} +48 q^{-10} +29 q^{-12} -83 q^{-14} +89 q^{-16} -47 q^{-18} -23 q^{-20} +92 q^{-22} -122 q^{-24} +101 q^{-26} -35 q^{-28} -53 q^{-30} +131 q^{-32} -173 q^{-34} +158 q^{-36} -91 q^{-38} -6 q^{-40} +98 q^{-42} -157 q^{-44} +157 q^{-46} -103 q^{-48} +19 q^{-50} +58 q^{-52} -102 q^{-54} +89 q^{-56} -33 q^{-58} -39 q^{-60} +90 q^{-62} -94 q^{-64} +49 q^{-66} +22 q^{-68} -90 q^{-70} +125 q^{-72} -111 q^{-74} +63 q^{-76} + q^{-78} -59 q^{-80} +88 q^{-82} -86 q^{-84} +64 q^{-86} -26 q^{-88} -5 q^{-90} +25 q^{-92} -33 q^{-94} +30 q^{-96} -21 q^{-98} +12 q^{-100} -2 q^{-102} -4 q^{-104} +5 q^{-106} -6 q^{-108} +4 q^{-110} -2 q^{-112} + q^{-114}