9 17

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9 16.gif

9_16

9 18.gif

9_18

Contents

9 17.gif
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Knot presentations

Planar diagram presentation X1425 X5,12,6,13 X3,11,4,10 X11,3,12,2 X7,14,8,15 X13,6,14,7 X15,18,16,1 X9,17,10,16 X17,9,18,8
Gauss code -1, 4, -3, 1, -2, 6, -5, 9, -8, 3, -4, 2, -6, 5, -7, 8, -9, 7
Dowker-Thistlethwaite code 4 10 12 14 16 2 6 18 8
Conway Notation [21312]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
BraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gif

Length is 9, width is 4,

Braid index is 4

9 17 ML.gif 9 17 AP.gif
[{11, 3}, {2, 9}, {10, 4}, {3, 5}, {9, 11}, {4, 6}, {5, 7}, {6, 1}, {8, 2}, {7, 10}, {1, 8}]

[edit Notes on presentations of 9 17]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 3
Bridge index 2
Super bridge index \{4,7\}
Nakanishi index 1
Maximal Thurston-Bennequin number [-8][-3]
Hyperbolic Volume 9.47458
A-Polynomial See Data:9 17/A-polynomial

[edit Notes for 9 17'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 9 17's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^3-5 t^2+9 t-9+9 t^{-1} -5 t^{-2} + t^{-3}
Conway polynomial z^6+z^4-2 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 39, -2 }
Jones polynomial q^3-2 q^2+4 q-5+6 q^{-1} -7 q^{-2} +6 q^{-3} -4 q^{-4} +3 q^{-5} - q^{-6}
HOMFLY-PT polynomial (db, data sources) a^2 z^6-a^4 z^4+4 a^2 z^4-2 z^4-2 a^4 z^2+5 a^2 z^2+z^2 a^{-2} -6 z^2+2 a^2+2 a^{-2} -3
Kauffman polynomial (db, data sources) a^2 z^8+z^8+3 a^3 z^7+5 a z^7+2 z^7 a^{-1} +4 a^4 z^6+4 a^2 z^6+z^6 a^{-2} +z^6+4 a^5 z^5-2 a^3 z^5-13 a z^5-7 z^5 a^{-1} +3 a^6 z^4-3 a^4 z^4-14 a^2 z^4-4 z^4 a^{-2} -12 z^4+a^7 z^3-3 a^5 z^3-4 a^3 z^3+6 a z^3+6 z^3 a^{-1} -2 a^6 z^2-a^4 z^2+9 a^2 z^2+5 z^2 a^{-2} +13 z^2+a^5 z+3 a^3 z+a z-z a^{-1} -2 a^2-2 a^{-2} -3
The A2 invariant -q^{18}+q^{16}+q^{12}+2 q^{10}-q^8+q^6-2 q^4- q^{-2} + q^{-4} + q^{-8} + q^{-10}
The G2 invariant q^{100}-2 q^{98}+3 q^{96}-4 q^{94}+q^{92}-3 q^{88}+8 q^{86}-9 q^{84}+12 q^{82}-9 q^{80}+3 q^{78}+4 q^{76}-9 q^{74}+14 q^{72}-20 q^{70}+17 q^{68}-12 q^{66}+q^{64}+10 q^{62}-18 q^{60}+22 q^{58}-16 q^{56}+8 q^{54}+q^{52}-14 q^{50}+16 q^{48}-7 q^{46}-2 q^{44}+15 q^{42}-18 q^{40}+15 q^{38}+3 q^{36}-17 q^{34}+30 q^{32}-35 q^{30}+26 q^{28}-6 q^{26}-14 q^{24}+33 q^{22}-38 q^{20}+32 q^{18}-16 q^{16}-4 q^{14}+15 q^{12}-26 q^{10}+22 q^8-12 q^6-4 q^4+14 q^2-17+10 q^{-2} +3 q^{-4} -17 q^{-6} +23 q^{-8} -24 q^{-10} +11 q^{-12} +5 q^{-14} -21 q^{-16} +32 q^{-18} -27 q^{-20} +17 q^{-22} - q^{-24} -11 q^{-26} +19 q^{-28} -18 q^{-30} +14 q^{-32} -4 q^{-34} -2 q^{-36} +5 q^{-38} -5 q^{-40} +4 q^{-42} - q^{-44} + q^{-46}