10 110

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10 109.gif

10_109

10 111.gif

10_111

Contents

10 110.gif
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Knot presentations

Planar diagram presentation X1627 X7,20,8,1 X3,11,4,10 X5,16,6,17 X17,8,18,9 X9,14,10,15 X11,3,12,2 X15,4,16,5 X13,19,14,18 X19,13,20,12
Gauss code -1, 7, -3, 8, -4, 1, -2, 5, -6, 3, -7, 10, -9, 6, -8, 4, -5, 9, -10, 2
Dowker-Thistlethwaite code 6 10 16 20 14 2 18 4 8 12
Conway Notation [2.2.2.20]


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

Length is 12, width is 5,

Braid index is 5

10 110 ML.gif 10 110 AP.gif
[{5, 3}, {2, 4}, {3, 1}, {6, 15}, {7, 5}, {11, 6}, {14, 8}, {9, 7}, {15, 12}, {8, 10}, {4, 9}, {13, 11}, {12, 2}, {10, 13}, {1, 14}]

[edit Notes on presentations of 10 110]


Three dimensional invariants

Symmetry type Chiral
Unknotting number 2
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-9][-3]
Hyperbolic Volume 14.7775
A-Polynomial See Data:10 110/A-polynomial

[edit Notes for 10 110'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 10 110's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^3-8 t^2+20 t-25+20 t^{-1} -8 t^{-2} + t^{-3}
Conway polynomial z^6-2 z^4-3 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 83, -2 }
Jones polynomial q^3-3 q^2+7 q-10+13 q^{-1} -14 q^{-2} +13 q^{-3} -11 q^{-4} +7 q^{-5} -3 q^{-6} + q^{-7}
HOMFLY-PT polynomial (db, data sources) z^2 a^6+a^6-2 z^4 a^4-3 z^2 a^4-a^4+z^6 a^2+2 z^4 a^2+z^2 a^2-2 z^4-3 z^2+z^2 a^{-2} + a^{-2}
Kauffman polynomial (db, data sources) 2 a^3 z^9+2 a z^9+6 a^4 z^8+10 a^2 z^8+4 z^8+8 a^5 z^7+9 a^3 z^7+4 a z^7+3 z^7 a^{-1} +6 a^6 z^6-5 a^4 z^6-20 a^2 z^6+z^6 a^{-2} -8 z^6+3 a^7 z^5-13 a^5 z^5-27 a^3 z^5-19 a z^5-8 z^5 a^{-1} +a^8 z^4-7 a^6 z^4-4 a^4 z^4+8 a^2 z^4-3 z^4 a^{-2} +z^4-2 a^7 z^3+12 a^5 z^3+21 a^3 z^3+13 a z^3+6 z^3 a^{-1} -a^8 z^2+5 a^6 z^2+6 a^4 z^2-a^2 z^2+3 z^2 a^{-2} +2 z^2-4 a^5 z-6 a^3 z-3 a z-z a^{-1} -a^6-a^4- a^{-2}
The A2 invariant q^{22}-q^{18}+3 q^{16}-2 q^{14}+q^{10}-3 q^8+2 q^6-3 q^4+2 q^2+1- q^{-2} +3 q^{-4} - q^{-6} + q^{-10}
The G2 invariant q^{114}-2 q^{112}+4 q^{110}-6 q^{108}+6 q^{106}-5 q^{104}+10 q^{100}-20 q^{98}+31 q^{96}-39 q^{94}+35 q^{92}-20 q^{90}-10 q^{88}+55 q^{86}-94 q^{84}+121 q^{82}-118 q^{80}+71 q^{78}+10 q^{76}-112 q^{74}+200 q^{72}-226 q^{70}+178 q^{68}-61 q^{66}-84 q^{64}+200 q^{62}-231 q^{60}+167 q^{58}-31 q^{56}-116 q^{54}+198 q^{52}-176 q^{50}+53 q^{48}+118 q^{46}-250 q^{44}+281 q^{42}-194 q^{40}+14 q^{38}+182 q^{36}-325 q^{34}+358 q^{32}-275 q^{30}+101 q^{28}+99 q^{26}-256 q^{24}+317 q^{22}-265 q^{20}+124 q^{18}+44 q^{16}-179 q^{14}+221 q^{12}-157 q^{10}+20 q^8+134 q^6-223 q^4+206 q^2-87-82 q^{-2} +226 q^{-4} -279 q^{-6} +228 q^{-8} -96 q^{-10} -60 q^{-12} +176 q^{-14} -213 q^{-16} +180 q^{-18} -94 q^{-20} +3 q^{-22} +60 q^{-24} -87 q^{-26} +76 q^{-28} -46 q^{-30} +19 q^{-32} +3 q^{-34} -12 q^{-36} +13 q^{-38} -10 q^{-40} +6 q^{-42} -2 q^{-44} + q^{-46}