10 32

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10 31.gif

10_31

10 33.gif

10_33

Contents

10 32.gif
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Knot presentations

Planar diagram presentation X1425 X3,12,4,13 X5,14,6,15 X15,20,16,1 X7,17,8,16 X19,7,20,6 X9,19,10,18 X17,9,18,8 X13,10,14,11 X11,2,12,3
Gauss code -1, 10, -2, 1, -3, 6, -5, 8, -7, 9, -10, 2, -9, 3, -4, 5, -8, 7, -6, 4
Dowker-Thistlethwaite code 4 12 14 16 18 2 10 20 8 6
Conway Notation [311122]


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

Length is 11, width is 4,

Braid index is 4

10 32 ML.gif 10 32 AP.gif
[{12, 4}, {3, 10}, {9, 11}, {10, 12}, {11, 5}, {4, 6}, {5, 2}, {8, 3}, {6, 1}, {7, 9}, {2, 8}, {1, 7}]

[edit Notes on presentations of 10 32]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 3
Bridge index 2
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-7][-5]
Hyperbolic Volume 12.0909
A-Polynomial See Data:10 32/A-polynomial

[edit Notes for 10 32's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 1
Topological 4 genus 1
Concordance genus 3
Rasmussen s-Invariant 0

[edit Notes for 10 32's four dimensional invariants]

Polynomial invariants

Alexander polynomial -2 t^3+8 t^2-15 t+19-15 t^{-1} +8 t^{-2} -2 t^{-3}
Conway polynomial -2 z^6-4 z^4-z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 69, 0 }
Jones polynomial q^4-3 q^3+6 q^2-9 q+11-11 q^{-1} +11 q^{-2} -8 q^{-3} +5 q^{-4} -3 q^{-5} + q^{-6}
HOMFLY-PT polynomial (db, data sources) -a^2 z^6-z^6+a^4 z^4-3 a^2 z^4+z^4 a^{-2} -3 z^4+2 a^4 z^2-2 a^2 z^2+2 z^2 a^{-2} -3 z^2+a^2+ a^{-2} -1
Kauffman polynomial (db, data sources) a^3 z^9+a z^9+3 a^4 z^8+6 a^2 z^8+3 z^8+3 a^5 z^7+5 a^3 z^7+7 a z^7+5 z^7 a^{-1} +a^6 z^6-7 a^4 z^6-10 a^2 z^6+5 z^6 a^{-2} +3 z^6-10 a^5 z^5-18 a^3 z^5-15 a z^5-4 z^5 a^{-1} +3 z^5 a^{-3} -3 a^6 z^4+3 a^4 z^4+2 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} -11 z^4+9 a^5 z^3+13 a^3 z^3+7 a z^3-3 z^3 a^{-3} +2 a^6 z^2+4 z^2 a^{-2} -z^2 a^{-4} +7 z^2-a^5 z-2 a^3 z-a z+z a^{-1} +z a^{-3} -a^2- a^{-2} -1
The A2 invariant q^{18}-q^{16}-2 q^{10}+3 q^8+q^4+q^2-2+2 q^{-2} -2 q^{-4} + q^{-6} + q^{-8} - q^{-10} + q^{-12}
The G2 invariant q^{94}-2 q^{92}+5 q^{90}-9 q^{88}+9 q^{86}-8 q^{84}-q^{82}+19 q^{80}-35 q^{78}+49 q^{76}-47 q^{74}+23 q^{72}+14 q^{70}-62 q^{68}+99 q^{66}-108 q^{64}+80 q^{62}-18 q^{60}-52 q^{58}+110 q^{56}-129 q^{54}+105 q^{52}-46 q^{50}-25 q^{48}+76 q^{46}-97 q^{44}+68 q^{42}-6 q^{40}-48 q^{38}+83 q^{36}-75 q^{34}+24 q^{32}+46 q^{30}-114 q^{28}+146 q^{26}-129 q^{24}+62 q^{22}+40 q^{20}-129 q^{18}+182 q^{16}-171 q^{14}+109 q^{12}-16 q^{10}-75 q^8+126 q^6-128 q^4+84 q^2-11-48 q^{-2} +72 q^{-4} -55 q^{-6} +4 q^{-8} +48 q^{-10} -84 q^{-12} +83 q^{-14} -50 q^{-16} -6 q^{-18} +65 q^{-20} -104 q^{-22} +113 q^{-24} -83 q^{-26} +37 q^{-28} +14 q^{-30} -58 q^{-32} +78 q^{-34} -76 q^{-36} +58 q^{-38} -25 q^{-40} -3 q^{-42} +23 q^{-44} -32 q^{-46} +30 q^{-48} -21 q^{-50} +12 q^{-52} -2 q^{-54} -4 q^{-56} +5 q^{-58} -6 q^{-60} +4 q^{-62} -2 q^{-64} + q^{-66}