K11a296

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K11a295.gif

K11a295

K11a297.gif

K11a297

K11a296.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

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Knot presentations

Planar diagram presentation X6271 X10,3,11,4 X16,5,17,6 X22,8,1,7 X18,9,19,10 X2,11,3,12 X20,13,21,14 X8,15,9,16 X4,17,5,18 X14,19,15,20 X12,21,13,22
Gauss code 1, -6, 2, -9, 3, -1, 4, -8, 5, -2, 6, -11, 7, -10, 8, -3, 9, -5, 10, -7, 11, -4
Dowker-Thistlethwaite code 6 10 16 22 18 2 20 8 4 14 12
A Braid Representative
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A Morse Link Presentation K11a296 ML.gif

Three dimensional invariants

Symmetry type Chiral
Unknotting number
3-genus 2
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11a296/ThurstonBennequinNumber
Hyperbolic Volume 15.7452
A-Polynomial See Data:K11a296/A-polynomial

[edit Notes for K11a296's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11a296's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 111, -2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a296/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a296/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

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

Vassiliev invariants

V2 and V3: (4, -10)
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 K11a296. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-9-8-7-6-5-4-3-2-1012χ
3           11
1          2 -2
-1         51 4
-3        83  -5
-5       84   4
-7      98    -1
-9     98     1
-11    69      3
-13   59       -4
-15  26        4
-17 15         -4
-19 2          2
-211           -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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K11a295.gif

K11a295

K11a297.gif

K11a297