9 48

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9 47.gif

9_47

9 49.gif

9_49

Contents

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Knot presentations

Planar diagram presentation X1425 X12,8,13,7 X3,11,4,10 X11,3,12,2 X14,6,15,5 X6,14,7,13 X15,18,16,1 X9,17,10,16 X17,9,18,8
Gauss code -1, 4, -3, 1, 5, -6, 2, 9, -8, 3, -4, -2, 6, -5, -7, 8, -9, 7
Dowker-Thistlethwaite code 4 10 -14 -12 16 2 -6 18 8
Conway Notation [21,21,21-]


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

Length is 11, width is 4,

Braid index is 4

9 48 ML.gif 9 48 AP.gif
[{10, 4}, {5, 3}, {4, 7}, {2, 5}, {8, 6}, {7, 1}, {3, 8}, {9, 2}, {6, 10}, {1, 9}]

[edit Notes on presentations of 9 48]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 2
Bridge index 3
Super bridge index \{4,6\}
Nakanishi index 2
Maximal Thurston-Bennequin number [-1][-8]
Hyperbolic Volume 9.53188
A-Polynomial See Data:9 48/A-polynomial

[edit Notes for 9 48'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 9 48's four dimensional invariants]

Polynomial invariants

Alexander polynomial -t^2+7 t-11+7 t^{-1} - t^{-2}
Conway polynomial -z^4+3 z^2+1
2nd Alexander ideal (db, data sources) \{3,t+1\}
Determinant and Signature { 27, 2 }
Jones polynomial -2 q^6+3 q^5-4 q^4+6 q^3-4 q^2+4 q-3+ q^{-1}
HOMFLY-PT polynomial (db, data sources) -z^4 a^{-2} -z^2 a^{-2} +3 z^2 a^{-4} +z^2+3 a^{-4} -2 a^{-6}
Kauffman polynomial (db, data sources) z^7 a^{-3} +z^7 a^{-5} +3 z^6 a^{-2} +4 z^6 a^{-4} +z^6 a^{-6} +3 z^5 a^{-1} +2 z^5 a^{-3} -z^5 a^{-5} -5 z^4 a^{-2} -6 z^4 a^{-4} +z^4-5 z^3 a^{-1} -3 z^3 a^{-3} +5 z^3 a^{-5} +3 z^3 a^{-7} +2 z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} -z^2-z a^{-3} -5 z a^{-5} -4 z a^{-7} +3 a^{-4} +2 a^{-6}
The A2 invariant q^4-q^2-1+ q^{-2} - q^{-4} +2 q^{-6} + q^{-8} +2 q^{-10} +2 q^{-12} + q^{-16} -2 q^{-18} -2 q^{-20}
The G2 invariant q^{18}-2 q^{16}+4 q^{14}-6 q^{12}+3 q^{10}+q^8-6 q^6+14 q^4-14 q^2+15-8 q^{-2} -7 q^{-4} +16 q^{-6} -23 q^{-8} +18 q^{-10} -9 q^{-12} -5 q^{-14} +13 q^{-16} -13 q^{-18} +10 q^{-20} + q^{-22} -13 q^{-24} +16 q^{-26} -13 q^{-28} + q^{-30} +15 q^{-32} -24 q^{-34} +27 q^{-36} -14 q^{-38} +11 q^{-40} +7 q^{-42} -22 q^{-44} +29 q^{-46} -22 q^{-48} +19 q^{-50} -2 q^{-52} -14 q^{-54} +21 q^{-56} -8 q^{-58} +6 q^{-60} + q^{-62} -15 q^{-64} +14 q^{-66} -5 q^{-68} -8 q^{-70} +14 q^{-72} -24 q^{-74} +21 q^{-76} -5 q^{-78} -10 q^{-80} +11 q^{-82} -18 q^{-84} +16 q^{-86} -9 q^{-88} -2 q^{-90} +3 q^{-92} -7 q^{-94} +7 q^{-96} -2 q^{-98} + q^{-100} + q^{-102}