K11n157

From Knot Atlas
Jump to navigationJump to search

K11n156.gif

K11n156

K11n158.gif

K11n158

K11n157.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n157 at Knotilus!



Knot presentations

Planar diagram presentation X6271 X3,11,4,10 X5,12,6,13 X14,7,15,8 X9,16,10,17 X11,19,12,18 X22,13,1,14 X20,16,21,15 X17,4,18,5 X19,3,20,2 X8,21,9,22
Gauss code 1, 10, -2, 9, -3, -1, 4, -11, -5, 2, -6, 3, 7, -4, 8, 5, -9, 6, -10, -8, 11, -7
Dowker-Thistlethwaite code 6 -10 -12 14 -16 -18 22 20 -4 -2 8
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart3.gif
BraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gif
A Morse Link Presentation K11n157 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11n157/ThurstonBennequinNumber
Hyperbolic Volume 14.7471
A-Polynomial See Data:K11n157/A-polynomial

[edit Notes for K11n157's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
Rasmussen s-Invariant 0

[edit Notes for K11n157's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 65, 0 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant
The G2 invariant Data:K11n157/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

Same Jones Polynomial (up to mirroring, ): {}

Vassiliev invariants

V2 and V3: (0, 0)
V2,1 through V6,9:
V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9

V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.

Khovanov Homology

The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where 0 is the signature of K11n157. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-6-5-4-3-2-10123χ
7         1-1
5        3 3
3       41 -3
1      63  3
-1     65   -1
-3    55    0
-5   46     2
-7  35      -2
-9 14       3
-11 3        -3
-131         1
Integral Khovanov Homology

(db, data source)

  

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.

Modifying This Page

Read me first: Modifying Knot Pages.

See/edit the Hoste-Thistlethwaite Knot Page master template (intermediate).

See/edit the Hoste-Thistlethwaite_Splice_Base (expert).

Back to the top.

K11n156.gif

K11n156

K11n158.gif

K11n158