10 44

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10 43.gif

10_43

10 45.gif

10_45

Contents

10 44.gif
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Knot presentations

Planar diagram presentation X1425 X5,12,6,13 X3,11,4,10 X11,3,12,2 X13,20,14,1 X9,15,10,14 X15,18,16,19 X7,16,8,17 X17,8,18,9 X19,7,20,6
Gauss code -1, 4, -3, 1, -2, 10, -8, 9, -6, 3, -4, 2, -5, 6, -7, 8, -9, 7, -10, 5
Dowker-Thistlethwaite code 4 10 12 16 14 2 20 18 8 6
Conway Notation [2121112]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
BraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart0.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 10, width is 5,

Braid index is 5

10 44 ML.gif 10 44 AP.gif
[{12, 6}, {5, 10}, {11, 7}, {6, 8}, {10, 12}, {7, 1}, {9, 5}, {3, 11}, {4, 2}, {8, 3}, {1, 4}, {2, 9}]

[edit Notes on presentations of 10 44]


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 [-9][-3]
Hyperbolic Volume 12.969
A-Polynomial See Data:10 44/A-polynomial

[edit Notes for 10 44'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 44's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^3-7 t^2+19 t-25+19 t^{-1} -7 t^{-2} + t^{-3}
Conway polynomial z^6-z^4+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 79, -2 }
Jones polynomial q^3-3 q^2+6 q-9+12 q^{-1} -13 q^{-2} +13 q^{-3} -10 q^{-4} +7 q^{-5} -4 q^{-6} + q^{-7}
HOMFLY-PT polynomial (db, data sources) z^2 a^6-2 z^4 a^4-3 z^2 a^4-a^4+z^6 a^2+3 z^4 a^2+5 z^2 a^2+3 a^2-2 z^4-4 z^2-2+z^2 a^{-2} + a^{-2}
Kauffman polynomial (db, data sources) a^3 z^9+a z^9+4 a^4 z^8+7 a^2 z^8+3 z^8+7 a^5 z^7+12 a^3 z^7+8 a z^7+3 z^7 a^{-1} +7 a^6 z^6+5 a^4 z^6-7 a^2 z^6+z^6 a^{-2} -4 z^6+4 a^7 z^5-6 a^5 z^5-27 a^3 z^5-26 a z^5-9 z^5 a^{-1} +a^8 z^4-8 a^6 z^4-18 a^4 z^4-12 a^2 z^4-3 z^4 a^{-2} -6 z^4-3 a^7 z^3+15 a^3 z^3+20 a z^3+8 z^3 a^{-1} +3 a^6 z^2+10 a^4 z^2+13 a^2 z^2+3 z^2 a^{-2} +9 z^2-2 a^3 z-4 a z-2 z a^{-1} -a^4-3 a^2- a^{-2} -2
The A2 invariant q^{22}-q^{20}-2 q^{18}+2 q^{16}-2 q^{14}+q^{12}+2 q^{10}-q^8+3 q^6-2 q^4+2 q^2-2 q^{-2} +2 q^{-4} - q^{-6} + q^{-10}
The G2 invariant q^{114}-3 q^{112}+6 q^{110}-10 q^{108}+9 q^{106}-6 q^{104}-2 q^{102}+19 q^{100}-33 q^{98}+50 q^{96}-54 q^{94}+36 q^{92}-5 q^{90}-41 q^{88}+88 q^{86}-122 q^{84}+127 q^{82}-93 q^{80}+23 q^{78}+63 q^{76}-138 q^{74}+176 q^{72}-161 q^{70}+92 q^{68}-2 q^{66}-90 q^{64}+139 q^{62}-122 q^{60}+57 q^{58}+35 q^{56}-103 q^{54}+114 q^{52}-60 q^{50}-44 q^{48}+151 q^{46}-212 q^{44}+199 q^{42}-102 q^{40}-43 q^{38}+188 q^{36}-273 q^{34}+272 q^{32}-185 q^{30}+40 q^{28}+103 q^{26}-197 q^{24}+219 q^{22}-156 q^{20}+50 q^{18}+60 q^{16}-124 q^{14}+119 q^{12}-52 q^{10}-43 q^8+124 q^6-153 q^4+113 q^2-20-91 q^{-2} +177 q^{-4} -199 q^{-6} +154 q^{-8} -64 q^{-10} -43 q^{-12} +121 q^{-14} -154 q^{-16} +137 q^{-18} -81 q^{-20} +15 q^{-22} +36 q^{-24} -63 q^{-26} +63 q^{-28} -44 q^{-30} +23 q^{-32} - q^{-34} -10 q^{-36} +12 q^{-38} -10 q^{-40} +6 q^{-42} -2 q^{-44} + q^{-46}