10 98

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10 97.gif

10_97

10 99.gif

10_99

Contents

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Knot presentations

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


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

Length is 11, width is 4,

Braid index is 4

10 98 ML.gif 10 98 AP.gif
[{13, 2}, {1, 9}, {8, 3}, {2, 7}, {6, 8}, {7, 10}, {9, 11}, {10, 4}, {12, 6}, {11, 13}, {3, 5}, {4, 12}, {5, 1}]

[edit Notes on presentations of 10 98]


Three dimensional invariants

Symmetry type Chiral
Unknotting number 2
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index 2
Maximal Thurston-Bennequin number [-13][1]
Hyperbolic Volume 14.4129
A-Polynomial See Data:10 98/A-polynomial

[edit Notes for 10 98's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for 10 98's four dimensional invariants]

Polynomial invariants

Alexander polynomial -2 t^3+9 t^2-18 t+23-18 t^{-1} +9 t^{-2} -2 t^{-3}
Conway polynomial -2 z^6-3 z^4+1
2nd Alexander ideal (db, data sources) \left\{t^2-t+1\right\}
Determinant and Signature { 81, -4 }
Jones polynomial 1-3 q^{-1} +7 q^{-2} -9 q^{-3} +13 q^{-4} -14 q^{-5} +12 q^{-6} -11 q^{-7} +7 q^{-8} -3 q^{-9} + q^{-10}
HOMFLY-PT polynomial (db, data sources) z^4 a^8+2 z^2 a^8+2 a^8-z^6 a^6-3 z^4 a^6-5 z^2 a^6-5 a^6-z^6 a^4-2 z^4 a^4+z^2 a^4+3 a^4+z^4 a^2+2 z^2 a^2+a^2
Kauffman polynomial (db, data sources) z^4 a^{12}-z^2 a^{12}+3 z^5 a^{11}-2 z^3 a^{11}+6 z^6 a^{10}-7 z^4 a^{10}+4 z^2 a^{10}+8 z^7 a^9-14 z^5 a^9+14 z^3 a^9-6 z a^9+6 z^8 a^8-7 z^6 a^8+2 z^4 a^8+2 a^8+2 z^9 a^7+8 z^7 a^7-26 z^5 a^7+25 z^3 a^7-12 z a^7+10 z^8 a^6-23 z^6 a^6+17 z^4 a^6-10 z^2 a^6+5 a^6+2 z^9 a^5+3 z^7 a^5-17 z^5 a^5+14 z^3 a^5-6 z a^5+4 z^8 a^4-9 z^6 a^4+4 z^4 a^4-2 z^2 a^4+3 a^4+3 z^7 a^3-8 z^5 a^3+5 z^3 a^3+z^6 a^2-3 z^4 a^2+3 z^2 a^2-a^2
The A2 invariant q^{30}-q^{28}+2 q^{26}+2 q^{24}-3 q^{22}-5 q^{18}-q^{16}+q^{14}+5 q^{10}-q^8+2 q^6+q^4-q^2+1
The G2 invariant q^{162}-2 q^{160}+4 q^{158}-6 q^{156}+6 q^{154}-5 q^{152}+10 q^{148}-21 q^{146}+31 q^{144}-39 q^{142}+33 q^{140}-18 q^{138}-12 q^{136}+58 q^{134}-94 q^{132}+117 q^{130}-107 q^{128}+56 q^{126}+17 q^{124}-112 q^{122}+185 q^{120}-203 q^{118}+154 q^{116}-41 q^{114}-84 q^{112}+183 q^{110}-192 q^{108}+134 q^{106}-19 q^{104}-110 q^{102}+175 q^{100}-143 q^{98}+34 q^{96}+116 q^{94}-230 q^{92}+256 q^{90}-161 q^{88}-7 q^{86}+163 q^{84}-297 q^{82}+322 q^{80}-242 q^{78}+78 q^{76}+92 q^{74}-232 q^{72}+288 q^{70}-230 q^{68}+90 q^{66}+43 q^{64}-158 q^{62}+191 q^{60}-129 q^{58}+8 q^{56}+128 q^{54}-194 q^{52}+181 q^{50}-68 q^{48}-83 q^{46}+204 q^{44}-244 q^{42}+197 q^{40}-81 q^{38}-51 q^{36}+157 q^{34}-188 q^{32}+162 q^{30}-84 q^{28}+3 q^{26}+51 q^{24}-78 q^{22}+69 q^{20}-44 q^{18}+20 q^{16}+2 q^{14}-11 q^{12}+13 q^{10}-10 q^8+6 q^6-2 q^4+q^2