10 11

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10 10.gif

10_10

10 12.gif

10_12

Contents

10 11.gif
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Knot presentations

Planar diagram presentation X1627 X11,16,12,17 X5,13,6,12 X3,15,4,14 X13,5,14,4 X15,3,16,2 X7,18,8,19 X9,20,10,1 X19,8,20,9 X17,10,18,11
Gauss code -1, 6, -4, 5, -3, 1, -7, 9, -8, 10, -2, 3, -5, 4, -6, 2, -10, 7, -9, 8
Dowker-Thistlethwaite code 6 14 12 18 20 16 4 2 10 8
Conway Notation [433]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
BraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gif

Length is 12, width is 5,

Braid index is 5

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

[edit Notes on presentations of 10 11]


Three dimensional invariants

Symmetry type Reversible
Unknotting number \{2,3\}
3-genus 2
Bridge index 2
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-9][-3]
Hyperbolic Volume 9.37044
A-Polynomial See Data:10 11/A-polynomial

[edit Notes for 10 11's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for 10 11's four dimensional invariants]

Polynomial invariants

Alexander polynomial -4 t^2+11 t-13+11 t^{-1} -4 t^{-2}
Conway polynomial -4 z^4-5 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 43, -2 }
Jones polynomial q^3-q^2+3 q-5+6 q^{-1} -7 q^{-2} +7 q^{-3} -6 q^{-4} +4 q^{-5} -2 q^{-6} + q^{-7}
HOMFLY-PT polynomial (db, data sources) z^2 a^6+a^6-z^4 a^4-z^2 a^4-2 z^4 a^2-4 z^2 a^2-a^2-z^4-2 z^2-1+z^2 a^{-2} +2 a^{-2}
Kauffman polynomial (db, data sources) a^3 z^9+a z^9+2 a^4 z^8+3 a^2 z^8+z^8+3 a^5 z^7-2 a^3 z^7-4 a z^7+z^7 a^{-1} +3 a^6 z^6-4 a^4 z^6-10 a^2 z^6+z^6 a^{-2} -2 z^6+2 a^7 z^5-7 a^5 z^5+5 a^3 z^5+11 a z^5-3 z^5 a^{-1} +a^8 z^4-6 a^6 z^4+5 a^4 z^4+16 a^2 z^4-5 z^4 a^{-2} -z^4-3 a^7 z^3+9 a^5 z^3-5 a^3 z^3-16 a z^3+z^3 a^{-1} -2 a^8 z^2+5 a^6 z^2-12 a^2 z^2+7 z^2 a^{-2} +2 z^2-2 a^5 z+2 a^3 z+5 a z+z a^{-1} -a^6+a^2-2 a^{-2} -1
The A2 invariant q^{22}+2 q^{16}-q^{14}-q^8+q^6-2 q^4-1- q^{-2} +2 q^{-4} + q^{-6} + q^{-8} + q^{-10}
The G2 invariant q^{114}-q^{112}+2 q^{110}-3 q^{108}+2 q^{106}-q^{104}-2 q^{102}+6 q^{100}-8 q^{98}+10 q^{96}-9 q^{94}+5 q^{92}+2 q^{90}-11 q^{88}+19 q^{86}-21 q^{84}+18 q^{82}-12 q^{80}-q^{78}+15 q^{76}-23 q^{74}+29 q^{72}-21 q^{70}+9 q^{68}+5 q^{66}-16 q^{64}+19 q^{62}-13 q^{60}+2 q^{58}+14 q^{56}-19 q^{54}+16 q^{52}+q^{50}-19 q^{48}+33 q^{46}-37 q^{44}+25 q^{42}-7 q^{40}-18 q^{38}+36 q^{36}-42 q^{34}+36 q^{32}-20 q^{30}-5 q^{28}+19 q^{26}-29 q^{24}+25 q^{22}-17 q^{20}+q^{18}+13 q^{16}-18 q^{14}+15 q^{12}-q^{10}-15 q^8+24 q^6-24 q^4+10 q^2+5-21 q^{-2} +31 q^{-4} -28 q^{-6} +19 q^{-8} -3 q^{-10} -14 q^{-12} +20 q^{-14} -19 q^{-16} +16 q^{-18} -8 q^{-20} + q^{-22} +5 q^{-24} -6 q^{-26} +9 q^{-28} -6 q^{-30} +4 q^{-32} +2 q^{-38} -2 q^{-40} +2 q^{-42} + q^{-46}