9 49

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9 48.gif

9_48

10 1.gif

10_1

Contents

9 49.gif
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Knot presentations

Planar diagram presentation X6271 X12,8,13,7 X5,15,6,14 X3,11,4,10 X11,3,12,2 X15,5,16,4 X17,9,18,8 X9,17,10,16 X18,14,1,13
Gauss code 1, 5, -4, 6, -3, -1, 2, 7, -8, 4, -5, -2, 9, 3, -6, 8, -7, -9
Dowker-Thistlethwaite code 6 -10 -14 12 -16 -2 18 -4 -8
Conway Notation [-20:-20:-20]


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

Length is 11, width is 4,

Braid index is 4

9 49 ML.gif 9 49 AP.gif
[{2, 7}, {1, 5}, {8, 3}, {7, 9}, {6, 2}, {4, 1}, {5, 8}, {3, 6}, {9, 4}]

[edit Notes on presentations of 9 49]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 3
3-genus 2
Bridge index 3
Super bridge index \{4,5\}
Nakanishi index 2
Maximal Thurston-Bennequin number [3][-12]
Hyperbolic Volume 9.42707
A-Polynomial See Data:9 49/A-polynomial

[edit Notes for 9 49'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 49's four dimensional invariants]

Polynomial invariants

Alexander polynomial 3 t^2-6 t+7-6 t^{-1} +3 t^{-2}
Conway polynomial 3 z^4+6 z^2+1
2nd Alexander ideal (db, data sources) \{5,t+1\}
Determinant and Signature { 25, 4 }
Jones polynomial -2 q^9+3 q^8-4 q^7+5 q^6-4 q^5+4 q^4-2 q^3+q^2
HOMFLY-PT polynomial (db, data sources) z^4 a^{-4} +2 z^4 a^{-6} +2 z^2 a^{-4} +6 z^2 a^{-6} -2 z^2 a^{-8} +4 a^{-6} -3 a^{-8}
Kauffman polynomial (db, data sources) z^7 a^{-7} +z^7 a^{-9} +3 z^6 a^{-6} +4 z^6 a^{-8} +z^6 a^{-10} +2 z^5 a^{-5} +z^5 a^{-7} -z^5 a^{-9} +z^4 a^{-4} -8 z^4 a^{-6} -9 z^4 a^{-8} -3 z^3 a^{-5} -3 z^3 a^{-7} +3 z^3 a^{-9} +3 z^3 a^{-11} -2 z^2 a^{-4} +9 z^2 a^{-6} +10 z^2 a^{-8} -z^2 a^{-10} +2 z a^{-7} -2 z a^{-9} -4 z a^{-11} -4 a^{-6} -3 a^{-8}
The A2 invariant  q^{-6} - q^{-8} + q^{-10} + q^{-14} +3 q^{-16} + q^{-18} +2 q^{-20} - q^{-22} - q^{-24} - q^{-26} -2 q^{-28}
The G2 invariant  q^{-30} - q^{-32} +2 q^{-34} -3 q^{-36} +2 q^{-38} - q^{-40} -2 q^{-42} +8 q^{-44} -10 q^{-46} +12 q^{-48} -7 q^{-50} - q^{-52} +10 q^{-54} -16 q^{-56} +19 q^{-58} -11 q^{-60} + q^{-62} +10 q^{-64} -14 q^{-66} +13 q^{-68} -2 q^{-70} -6 q^{-72} +14 q^{-74} -12 q^{-76} +4 q^{-78} +9 q^{-80} -15 q^{-82} +21 q^{-84} -16 q^{-86} +9 q^{-88} +5 q^{-90} -13 q^{-92} +22 q^{-94} -22 q^{-96} +16 q^{-98} -4 q^{-100} -7 q^{-102} +13 q^{-104} -16 q^{-106} +9 q^{-108} - q^{-110} -10 q^{-112} +10 q^{-114} -11 q^{-116} -2 q^{-118} +10 q^{-120} -20 q^{-122} +16 q^{-124} -9 q^{-126} -4 q^{-128} +11 q^{-130} -16 q^{-132} +15 q^{-134} -7 q^{-136} + q^{-138} +3 q^{-140} -7 q^{-142} +7 q^{-144} -2 q^{-146} + q^{-148} + q^{-150}