9 30

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9 29.gif

9_29

9 31.gif

9_31

Contents

9 30.gif
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Knot presentations

Planar diagram presentation X4251 X10,6,11,5 X8394 X2,9,3,10 X14,8,15,7 X18,15,1,16 X16,11,17,12 X12,17,13,18 X6,14,7,13
Gauss code 1, -4, 3, -1, 2, -9, 5, -3, 4, -2, 7, -8, 9, -5, 6, -7, 8, -6
Dowker-Thistlethwaite code 4 8 10 14 2 16 6 18 12
Conway Notation [211,21,2]


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

Length is 9, width is 4,

Braid index is 4

9 30 ML.gif 9 30 AP.gif
[{2, 12}, {1, 6}, {11, 4}, {12, 10}, {8, 11}, {7, 9}, {6, 8}, {3, 5}, {4, 7}, {5, 2}, {9, 3}, {10, 1}]

[edit Notes on presentations of 9 30]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 3
Bridge index 3
Super bridge index \{4,6\}
Nakanishi index 1
Maximal Thurston-Bennequin number [-6][-5]
Hyperbolic Volume 11.9545
A-Polynomial See Data:9 30/A-polynomial

[edit Notes for 9 30's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 1
Topological 4 genus 1
Concordance genus 3
Rasmussen s-Invariant 0

[edit Notes for 9 30's four dimensional invariants]

Polynomial invariants

Alexander polynomial -t^3+5 t^2-12 t+17-12 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 { 53, 0 }
Jones polynomial q^4-3 q^3+6 q^2-8 q+9-9 q^{-1} +8 q^{-2} -5 q^{-3} +3 q^{-4} - q^{-5}
HOMFLY-PT polynomial (db, data sources) -z^6+2 a^2 z^4+z^4 a^{-2} -4 z^4-a^4 z^2+5 a^2 z^2+2 z^2 a^{-2} -7 z^2-a^4+4 a^2+2 a^{-2} -4
Kauffman polynomial (db, data sources) a^2 z^8+z^8+3 a^3 z^7+7 a z^7+4 z^7 a^{-1} +3 a^4 z^6+8 a^2 z^6+5 z^6 a^{-2} +10 z^6+a^5 z^5-3 a^3 z^5-9 a z^5-2 z^5 a^{-1} +3 z^5 a^{-3} -7 a^4 z^4-22 a^2 z^4-7 z^4 a^{-2} +z^4 a^{-4} -23 z^4-2 a^5 z^3-3 a^3 z^3-2 z^3 a^{-1} -3 z^3 a^{-3} +5 a^4 z^2+16 a^2 z^2+5 z^2 a^{-2} -z^2 a^{-4} +17 z^2+a^5 z+2 a^3 z+a z+z a^{-1} +z a^{-3} -a^4-4 a^2-2 a^{-2} -4
The A2 invariant -q^{16}+q^{12}-q^{10}+3 q^8+q^6+q^2-3+ q^{-2} -2 q^{-4} + q^{-6} +2 q^{-8} - q^{-10} + q^{-12}
The G2 invariant q^{80}-2 q^{78}+5 q^{76}-8 q^{74}+7 q^{72}-5 q^{70}-5 q^{68}+19 q^{66}-31 q^{64}+39 q^{62}-34 q^{60}+11 q^{58}+19 q^{56}-55 q^{54}+79 q^{52}-79 q^{50}+49 q^{48}-2 q^{46}-48 q^{44}+83 q^{42}-84 q^{40}+60 q^{38}-9 q^{36}-36 q^{34}+61 q^{32}-52 q^{30}+14 q^{28}+39 q^{26}-69 q^{24}+75 q^{22}-40 q^{20}-15 q^{18}+77 q^{16}-118 q^{14}+120 q^{12}-84 q^{10}+16 q^8+55 q^6-109 q^4+123 q^2-97+43 q^{-2} +15 q^{-4} -64 q^{-6} +72 q^{-8} -52 q^{-10} +6 q^{-12} +39 q^{-14} -60 q^{-16} +48 q^{-18} -8 q^{-20} -41 q^{-22} +79 q^{-24} -87 q^{-26} +65 q^{-28} -21 q^{-30} -29 q^{-32} +67 q^{-34} -77 q^{-36} +67 q^{-38} -34 q^{-40} +5 q^{-42} +19 q^{-44} -33 q^{-46} +32 q^{-48} -23 q^{-50} +13 q^{-52} -2 q^{-54} -4 q^{-56} +5 q^{-58} -6 q^{-60} +4 q^{-62} -2 q^{-64} + q^{-66}