9 5

From Knot Atlas
Jump to: navigation, search

9 4.gif

9_4

9 6.gif

9_6

Contents

9 5.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

Visit 9 5's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit 9 5 at Knotilus!


Knot presentations

Planar diagram presentation X6271 X14,6,15,5 X18,8,1,7 X16,10,17,9 X10,16,11,15 X8,18,9,17 X2,14,3,13 X12,4,13,3 X4,12,5,11
Gauss code 1, -7, 8, -9, 2, -1, 3, -6, 4, -5, 9, -8, 7, -2, 5, -4, 6, -3
Dowker-Thistlethwaite code 6 12 14 18 16 4 2 10 8
Conway Notation [513]


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

Length is 12, width is 5,

Braid index is 5

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

[edit Notes on presentations of 9 5]

Knot 9_5.
A graph, knot 9_5.

Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 1
Bridge index 2
Super bridge index \{4,6\}
Nakanishi index 1
Maximal Thurston-Bennequin number [1][-12]
Hyperbolic Volume 5.69844
A-Polynomial See Data:9 5/A-polynomial

[edit Notes for 9 5's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 1
Topological 4 genus 1
Concordance genus 1
Rasmussen s-Invariant -2

[edit Notes for 9 5's four dimensional invariants]

Polynomial invariants

Alexander polynomial 6 t-11+6 t^{-1}
Conway polynomial 6 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 23, 2 }
Jones polynomial -q^{10}+q^9-2 q^8+3 q^7-3 q^6+4 q^5-3 q^4+3 q^3-2 q^2+q
HOMFLY-PT polynomial (db, data sources) z^2 a^{-2} +2 z^2 a^{-4} +2 z^2 a^{-6} +z^2 a^{-8} + a^{-4} + a^{-6} - a^{-10}
Kauffman polynomial (db, data sources) z^8 a^{-8} +z^8 a^{-10} +2 z^7 a^{-7} +3 z^7 a^{-9} +z^7 a^{-11} +3 z^6 a^{-6} -2 z^6 a^{-8} -5 z^6 a^{-10} +3 z^5 a^{-5} -5 z^5 a^{-7} -14 z^5 a^{-9} -6 z^5 a^{-11} +3 z^4 a^{-4} -7 z^4 a^{-6} -3 z^4 a^{-8} +7 z^4 a^{-10} +2 z^3 a^{-3} -4 z^3 a^{-5} +z^3 a^{-7} +18 z^3 a^{-9} +11 z^3 a^{-11} +z^2 a^{-2} -3 z^2 a^{-4} +3 z^2 a^{-6} +4 z^2 a^{-8} -3 z^2 a^{-10} -6 z a^{-9} -6 z a^{-11} + a^{-4} - a^{-6} + a^{-10}
The A2 invariant  q^{-2} - q^{-4} + q^{-8} + q^{-12} + q^{-14} + q^{-16} + q^{-18} + q^{-22} - q^{-26} - q^{-30} - q^{-32}
The G2 invariant  q^{-10} - q^{-12} + q^{-14} - q^{-16} - q^{-22} +3 q^{-24} -2 q^{-26} +2 q^{-28} - q^{-30} + q^{-34} - q^{-36} +3 q^{-38} -2 q^{-40} + q^{-42} +2 q^{-48} - q^{-50} + q^{-52} - q^{-54} + q^{-56} - q^{-60} + q^{-62} + q^{-66} + q^{-72} + q^{-74} +2 q^{-78} -2 q^{-80} +5 q^{-82} - q^{-84} - q^{-86} +5 q^{-88} -4 q^{-90} +6 q^{-92} -2 q^{-94} - q^{-96} +3 q^{-98} -2 q^{-100} +4 q^{-102} -3 q^{-104} - q^{-110} + q^{-112} -2 q^{-114} - q^{-116} + q^{-118} -3 q^{-120} -2 q^{-124} -2 q^{-126} +3 q^{-128} -6 q^{-130} +3 q^{-132} -2 q^{-134} -2 q^{-136} +4 q^{-138} -5 q^{-140} +3 q^{-142} - q^{-144} + q^{-148} -2 q^{-150} +2 q^{-152} + q^{-156}