9 29

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9 28.gif

9_28

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9_30

Contents

9 29.gif
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Knot presentations

Planar diagram presentation X6271 X16,11,17,12 X10,4,11,3 X2,15,3,16 X14,5,15,6 X18,8,1,7 X4,10,5,9 X12,17,13,18 X8,13,9,14
Gauss code 1, -4, 3, -7, 5, -1, 6, -9, 7, -3, 2, -8, 9, -5, 4, -2, 8, -6
Dowker-Thistlethwaite code 6 10 14 18 4 16 8 2 12
Conway Notation [.2.20.2]


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

Length is 9, width is 4,

Braid index is 4

9 29 ML.gif 9 29 AP.gif
[{2, 4}, {1, 3}, {12, 5}, {4, 9}, {10, 6}, {5, 7}, {9, 11}, {6, 8}, {7, 2}, {3, 10}, {8, 12}, {11, 1}]

[edit Notes on presentations of 9 29]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 3
Bridge index 3
Super bridge index \{4,7\}
Nakanishi index 1
Maximal Thurston-Bennequin number [-8][-3]
Hyperbolic Volume 12.2059
A-Polynomial See Data:9 29/A-polynomial

[edit Notes for 9 29'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 29's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^3-5 t^2+12 t-15+12 t^{-1} -5 t^{-2} + t^{-3}
Conway polynomial z^6+z^4+z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 51, -2 }
Jones polynomial q^3-3 q^2+5 q-7+9 q^{-1} -8 q^{-2} +8 q^{-3} -6 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+7 a^2 z^2+z^2 a^{-2} -5 z^2-2 a^4+5 a^2+ a^{-2} -3
Kauffman polynomial (db, data sources) 2 a^2 z^8+2 z^8+6 a^3 z^7+9 a z^7+3 z^7 a^{-1} +8 a^4 z^6+6 a^2 z^6+z^6 a^{-2} -z^6+6 a^5 z^5-8 a^3 z^5-24 a z^5-10 z^5 a^{-1} +3 a^6 z^4-13 a^4 z^4-24 a^2 z^4-3 z^4 a^{-2} -11 z^4+a^7 z^3-5 a^5 z^3-a^3 z^3+14 a z^3+9 z^3 a^{-1} +8 a^4 z^2+17 a^2 z^2+3 z^2 a^{-2} +12 z^2+2 a^5 z+2 a^3 z-a z-z a^{-1} -2 a^4-5 a^2- a^{-2} -3
The A2 invariant -q^{18}+q^{16}-2 q^{14}-q^{12}+2 q^{10}+4 q^6+q^2-2 q^{-2} + q^{-4} - q^{-6} + q^{-10}
The G2 invariant q^{100}-2 q^{98}+3 q^{96}-4 q^{94}+3 q^{92}-2 q^{90}-q^{88}+8 q^{86}-12 q^{84}+16 q^{82}-19 q^{80}+13 q^{78}-6 q^{76}-9 q^{74}+28 q^{72}-39 q^{70}+44 q^{68}-37 q^{66}+16 q^{64}+13 q^{62}-46 q^{60}+63 q^{58}-61 q^{56}+31 q^{54}+5 q^{52}-41 q^{50}+57 q^{48}-42 q^{46}+9 q^{44}+30 q^{42}-59 q^{40}+56 q^{38}-21 q^{36}-30 q^{34}+78 q^{32}-91 q^{30}+77 q^{28}-24 q^{26}-29 q^{24}+77 q^{22}-96 q^{20}+88 q^{18}-50 q^{16}+47 q^{12}-69 q^{10}+69 q^8-36 q^6-5 q^4+36 q^2-55+41 q^{-2} -7 q^{-4} -39 q^{-6} +68 q^{-8} -70 q^{-10} +39 q^{-12} +10 q^{-14} -56 q^{-16} +77 q^{-18} -70 q^{-20} +40 q^{-22} -3 q^{-24} -32 q^{-26} +47 q^{-28} -40 q^{-30} +27 q^{-32} -6 q^{-34} -7 q^{-36} +11 q^{-38} -10 q^{-40} +6 q^{-42} -2 q^{-44} + q^{-46}