9 38

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9 37.gif

9_37

9 39.gif

9_39

Contents

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Knot presentations

Planar diagram presentation X1627 X5,14,6,15 X7,18,8,1 X15,8,16,9 X3,10,4,11 X9,4,10,5 X17,12,18,13 X11,16,12,17 X13,2,14,3
Gauss code -1, 9, -5, 6, -2, 1, -3, 4, -6, 5, -8, 7, -9, 2, -4, 8, -7, 3
Dowker-Thistlethwaite code 6 10 14 18 4 16 2 8 12
Conway Notation [.2.2.2]


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.gifBraidPart0.gifBraidPart0.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart3.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart0.gif

Length is 11, width is 4,

Braid index is 4

9 38 ML.gif 9 38 AP.gif
[{11, 4}, {3, 9}, {4, 2}, {5, 10}, {6, 3}, {8, 5}, {1, 6}, {9, 7}, {2, 8}, {7, 11}, {10, 1}]

[edit Notes on presentations of 9 38]


Three dimensional invariants

Symmetry type Reversible
Unknotting number \{2,3\}
3-genus 2
Bridge index 3
Super bridge index \{4,7\}
Nakanishi index 2
Maximal Thurston-Bennequin number [-14][3]
Hyperbolic Volume 12.9329
A-Polynomial See Data:9 38/A-polynomial

[edit Notes for 9 38'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 9 38's four dimensional invariants]

Polynomial invariants

Alexander polynomial 5 t^2-14 t+19-14 t^{-1} +5 t^{-2}
Conway polynomial 5 z^4+6 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 57, -4 }
Jones polynomial  q^{-2} -3 q^{-3} +7 q^{-4} -8 q^{-5} +10 q^{-6} -10 q^{-7} +8 q^{-8} -6 q^{-9} +3 q^{-10} - q^{-11}
HOMFLY-PT polynomial (db, data sources) -z^2 a^{10}+z^4 a^8-z^2 a^8-3 a^8+3 z^4 a^6+7 z^2 a^6+4 a^6+z^4 a^4+z^2 a^4
Kauffman polynomial (db, data sources) z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-6 z^4 a^{12}+3 z^2 a^{12}+4 z^7 a^{11}-7 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+2 z^8 a^{10}+3 z^6 a^{10}-10 z^4 a^{10}+3 z^2 a^{10}+9 z^7 a^9-15 z^5 a^9+5 z^3 a^9+z a^9+2 z^8 a^8+6 z^6 a^8-15 z^4 a^8+10 z^2 a^8-3 a^8+5 z^7 a^7-4 z^5 a^7-2 z^3 a^7+3 z a^7+6 z^6 a^6-10 z^4 a^6+9 z^2 a^6-4 a^6+3 z^5 a^5-2 z^3 a^5+z^4 a^4-z^2 a^4
The A2 invariant -q^{34}+q^{32}+q^{30}-3 q^{28}-2 q^{24}-q^{22}+2 q^{20}+4 q^{16}+q^{12}+2 q^{10}-2 q^8+q^6
The G2 invariant q^{176}-2 q^{174}+5 q^{172}-8 q^{170}+8 q^{168}-6 q^{166}-2 q^{164}+18 q^{162}-33 q^{160}+47 q^{158}-46 q^{156}+21 q^{154}+16 q^{152}-65 q^{150}+101 q^{148}-104 q^{146}+70 q^{144}-6 q^{142}-63 q^{140}+112 q^{138}-116 q^{136}+77 q^{134}-8 q^{132}-60 q^{130}+87 q^{128}-70 q^{126}+15 q^{124}+52 q^{122}-95 q^{120}+98 q^{118}-56 q^{116}-20 q^{114}+93 q^{112}-152 q^{110}+153 q^{108}-105 q^{106}+19 q^{104}+69 q^{102}-137 q^{100}+159 q^{98}-125 q^{96}+52 q^{94}+26 q^{92}-90 q^{90}+105 q^{88}-66 q^{86}+q^{84}+64 q^{82}-84 q^{80}+67 q^{78}-9 q^{76}-58 q^{74}+106 q^{72}-112 q^{70}+82 q^{68}-20 q^{66}-43 q^{64}+89 q^{62}-94 q^{60}+77 q^{58}-36 q^{56}+25 q^{52}-40 q^{50}+37 q^{48}-25 q^{46}+13 q^{44}-5 q^{40}+6 q^{38}-6 q^{36}+4 q^{34}-2 q^{32}+q^{30}