K11a337

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K11a336.gif

K11a336

K11a338.gif

K11a338

K11a337.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

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Knot presentations

Planar diagram presentation X6271 X14,4,15,3 X16,6,17,5 X18,8,19,7 X20,10,21,9 X22,12,1,11 X4,14,5,13 X2,16,3,15 X12,18,13,17 X10,20,11,19 X8,22,9,21
Gauss code 1, -8, 2, -7, 3, -1, 4, -11, 5, -10, 6, -9, 7, -2, 8, -3, 9, -4, 10, -5, 11, -6
Dowker-Thistlethwaite code 6 14 16 18 20 22 4 2 12 10 8
A Braid Representative
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A Morse Link Presentation K11a337 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number
3-genus 2
Bridge index 2
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11a337/ThurstonBennequinNumber
Hyperbolic Volume 12.7191
A-Polynomial See Data:K11a337/A-polynomial

[edit Notes for K11a337's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11a337's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 89, 4 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a337/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a337/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

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

Vassiliev invariants

V2 and V3: (10, 31)
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 4 is the signature of K11a337. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
01234567891011χ
27           1-1
25          1 1
23         41 -3
21        41  3
19       74   -3
17      74    3
15     77     0
13    67      -1
11   47       3
9  36        -3
7  4         4
513          -2
31           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).

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K11a336.gif

K11a336

K11a338.gif

K11a338