K11a323

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K11a322.gif

K11a322

K11a324.gif

K11a324

K11a323.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a323 at Knotilus!



Knot presentations

Planar diagram presentation X6271 X12,4,13,3 X16,5,17,6 X22,8,1,7 X20,10,21,9 X4,12,5,11 X18,13,19,14 X10,15,11,16 X2,17,3,18 X14,19,15,20 X8,22,9,21
Gauss code 1, -9, 2, -6, 3, -1, 4, -11, 5, -8, 6, -2, 7, -10, 8, -3, 9, -7, 10, -5, 11, -4
Dowker-Thistlethwaite code 6 12 16 22 20 4 18 10 2 14 8
A Braid Representative
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A Morse Link Presentation K11a323 ML.gif

Three dimensional invariants

Symmetry type Chiral
Unknotting number
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11a323/ThurstonBennequinNumber
Hyperbolic Volume 13.4473
A-Polynomial See Data:K11a323/A-polynomial

[edit Notes for K11a323's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11a323's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 83, -2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a323/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a323/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {10_83, K11a307,}

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

Vassiliev invariants

V2 and V3: (1, -2)
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 -2 is the signature of K11a323. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-5-4-3-2-10123456χ
11           11
9          2 -2
7         31 2
5        52  -3
3       63   3
1      65    -1
-1     76     1
-3    57      2
-5   46       -2
-7  25        3
-9 14         -3
-11 2          2
-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.

K11a322.gif

K11a322

K11a324.gif

K11a324