10 7

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10 6.gif

10_6

10 8.gif

10_8

Contents

10 7.gif
(KnotPlot image)

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Knot presentations

Planar diagram presentation X1425 X5,14,6,15 X3,13,4,12 X13,3,14,2 X11,20,12,1 X19,6,20,7 X7,18,8,19 X9,16,10,17 X15,10,16,11 X17,8,18,9
Gauss code -1, 4, -3, 1, -2, 6, -7, 10, -8, 9, -5, 3, -4, 2, -9, 8, -10, 7, -6, 5
Dowker-Thistlethwaite code 4 12 14 18 16 20 2 10 8 6
Conway Notation [5212]


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

Length is 12, width is 5,

Braid index is 5

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

[edit Notes on presentations of 10 7]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 2
Bridge index 2
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-11][-1]
Hyperbolic Volume 9.11591
A-Polynomial See Data:10 7/A-polynomial

[edit Notes for 10 7'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 7's four dimensional invariants]

Polynomial invariants

Alexander polynomial -3 t^2+11 t-15+11 t^{-1} -3 t^{-2}
Conway polynomial -3 z^4-z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 43, -2 }
Jones polynomial q-2+4 q^{-1} -5 q^{-2} +7 q^{-3} -7 q^{-4} +6 q^{-5} -5 q^{-6} +3 q^{-7} -2 q^{-8} + q^{-9}
HOMFLY-PT polynomial (db, data sources) z^2 a^8+a^8-z^4 a^6-2 z^2 a^6-2 a^6-z^4 a^4+a^4-z^4 a^2-z^2 a^2+z^2+1
Kauffman polynomial (db, data sources) z^6 a^{10}-4 z^4 a^{10}+3 z^2 a^{10}+2 z^7 a^9-8 z^5 a^9+8 z^3 a^9-3 z a^9+2 z^8 a^8-7 z^6 a^8+6 z^4 a^8-3 z^2 a^8+a^8+z^9 a^7-z^7 a^7-6 z^5 a^7+10 z^3 a^7-5 z a^7+4 z^8 a^6-15 z^6 a^6+20 z^4 a^6-10 z^2 a^6+2 a^6+z^9 a^5-z^7 a^5-2 z^5 a^5+6 z^3 a^5-2 z a^5+2 z^8 a^4-5 z^6 a^4+8 z^4 a^4-4 z^2 a^4+a^4+2 z^7 a^3-2 z^5 a^3+z^3 a^3+2 z^6 a^2-z^4 a^2-2 z^2 a^2+2 z^5 a-3 z^3 a+z^4-2 z^2+1
The A2 invariant q^{28}+q^{22}-2 q^{20}-q^{18}-q^{14}+q^{12}+q^8+q^6-q^4+2 q^2+ q^{-4}
The G2 invariant q^{142}-q^{140}+2 q^{138}-3 q^{136}+2 q^{134}-3 q^{132}-q^{130}+6 q^{128}-10 q^{126}+12 q^{124}-12 q^{122}+8 q^{120}+2 q^{118}-12 q^{116}+22 q^{114}-24 q^{112}+21 q^{110}-8 q^{108}-7 q^{106}+20 q^{104}-23 q^{102}+22 q^{100}-9 q^{98}-4 q^{96}+14 q^{94}-16 q^{92}+8 q^{90}+2 q^{88}-14 q^{86}+19 q^{84}-16 q^{82}+q^{80}+10 q^{78}-23 q^{76}+27 q^{74}-25 q^{72}+11 q^{70}+2 q^{68}-19 q^{66}+29 q^{64}-30 q^{62}+21 q^{60}-6 q^{58}-8 q^{56}+18 q^{54}-20 q^{52}+15 q^{50}-3 q^{48}-6 q^{46}+11 q^{44}-8 q^{42}+q^{40}+10 q^{38}-14 q^{36}+14 q^{34}-7 q^{32}-2 q^{30}+9 q^{28}-14 q^{26}+16 q^{24}-13 q^{22}+9 q^{20}-2 q^{18}-5 q^{16}+10 q^{14}-12 q^{12}+14 q^{10}-10 q^8+6 q^6-6 q^2+9-8 q^{-2} +7 q^{-4} -3 q^{-6} + q^{-8} +2 q^{-10} -3 q^{-12} +3 q^{-14} - q^{-16} + q^{-18}