10 38

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10 37.gif

10_37

10 39.gif

10_39

Contents

10 38.gif
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Knot presentations

Planar diagram presentation X1425 X3,10,4,11 X5,12,6,13 X15,18,16,19 X7,17,8,16 X17,7,18,6 X13,20,14,1 X19,14,20,15 X11,8,12,9 X9,2,10,3
Gauss code -1, 10, -2, 1, -3, 6, -5, 9, -10, 2, -9, 3, -7, 8, -4, 5, -6, 4, -8, 7
Dowker-Thistlethwaite code 4 10 12 16 2 8 20 18 6 14
Conway Notation [23122]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
BraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.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 38 ML.gif 10 38 AP.gif
[{12, 5}, {4, 10}, {9, 11}, {10, 12}, {11, 6}, {5, 7}, {6, 3}, {2, 4}, {3, 1}, {8, 2}, {7, 9}, {1, 8}]

[edit Notes on presentations of 10 38]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 2
Bridge index 2
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-11][-1]
Hyperbolic Volume 11.3493
A-Polynomial See Data:10 38/A-polynomial

[edit Notes for 10 38'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 38's four dimensional invariants]

Polynomial invariants

Alexander polynomial -4 t^2+15 t-21+15 t^{-1} -4 t^{-2}
Conway polynomial -4 z^4-z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 59, -2 }
Jones polynomial q-2+5 q^{-1} -7 q^{-2} +9 q^{-3} -10 q^{-4} +9 q^{-5} -7 q^{-6} +5 q^{-7} -3 q^{-8} + q^{-9}
HOMFLY-PT polynomial (db, data sources) z^2 a^8-z^4 a^6+a^6-2 z^4 a^4-3 z^2 a^4-2 a^4-z^4 a^2+a^2+z^2+1
Kauffman polynomial (db, data sources) z^6 a^{10}-3 z^4 a^{10}+2 z^2 a^{10}+3 z^7 a^9-10 z^5 a^9+8 z^3 a^9-z a^9+3 z^8 a^8-8 z^6 a^8+4 z^4 a^8+z^9 a^7+3 z^7 a^7-13 z^5 a^7+8 z^3 a^7-z a^7+5 z^8 a^6-10 z^6 a^6+3 z^4 a^6+2 z^2 a^6-a^6+z^9 a^5+3 z^7 a^5-7 z^5 a^5+3 z^3 a^5+2 z^8 a^4+2 z^6 a^4-8 z^4 a^4+8 z^2 a^4-2 a^4+3 z^7 a^3-2 z^5 a^3+z^3 a^3+3 z^6 a^2-3 z^4 a^2+2 z^2 a^2-a^2+2 z^5 a-2 z^3 a+z^4-2 z^2+1
The A2 invariant q^{28}-q^{26}-q^{24}+2 q^{22}-q^{20}+q^{18}+q^{16}-2 q^{14}-2 q^{10}+q^8+q^6-q^4+3 q^2+ q^{-4}
The G2 invariant q^{142}-2 q^{140}+5 q^{138}-9 q^{136}+9 q^{134}-7 q^{132}-3 q^{130}+20 q^{128}-33 q^{126}+41 q^{124}-36 q^{122}+12 q^{120}+20 q^{118}-55 q^{116}+77 q^{114}-70 q^{112}+40 q^{110}+6 q^{108}-49 q^{106}+73 q^{104}-70 q^{102}+40 q^{100}-35 q^{96}+51 q^{94}-39 q^{92}+8 q^{90}+32 q^{88}-53 q^{86}+54 q^{84}-32 q^{82}-12 q^{80}+55 q^{78}-87 q^{76}+94 q^{74}-64 q^{72}+15 q^{70}+44 q^{68}-89 q^{66}+101 q^{64}-81 q^{62}+35 q^{60}+13 q^{58}-54 q^{56}+65 q^{54}-46 q^{52}+12 q^{50}+21 q^{48}-40 q^{46}+30 q^{44}-7 q^{42}-26 q^{40}+46 q^{38}-50 q^{36}+40 q^{34}-12 q^{32}-19 q^{30}+43 q^{28}-54 q^{26}+52 q^{24}-35 q^{22}+14 q^{20}+8 q^{18}-26 q^{16}+37 q^{14}-35 q^{12}+29 q^{10}-13 q^8+q^6+9 q^4-15 q^2+15-11 q^{-2} +8 q^{-4} -2 q^{-6} - q^{-8} +3 q^{-10} -3 q^{-12} +3 q^{-14} - q^{-16} + q^{-18}