K11a67

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K11a66.gif

K11a66

K11a68.gif

K11a68

K11a67.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

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Knot presentations

Planar diagram presentation X4251 X8394 X16,5,17,6 X12,8,13,7 X2,9,3,10 X18,12,19,11 X22,13,1,14 X20,15,21,16 X10,18,11,17 X6,19,7,20 X14,21,15,22
Gauss code 1, -5, 2, -1, 3, -10, 4, -2, 5, -9, 6, -4, 7, -11, 8, -3, 9, -6, 10, -8, 11, -7
Dowker-Thistlethwaite code 4 8 16 12 2 18 22 20 10 6 14
A Braid Representative
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A Morse Link Presentation K11a67 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:K11a67/ThurstonBennequinNumber
Hyperbolic Volume 16.0998
A-Polynomial See Data:K11a67/A-polynomial

[edit Notes for K11a67's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11a67's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 125, 0 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a67/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a67/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11a104, K11a168,}

Same Jones Polynomial (up to mirroring, ): {K11a317,}

Vassiliev invariants

V2 and V3: (1, -3)
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 K11a67. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-7-6-5-4-3-2-101234χ
9           11
7          3 -3
5         61 5
3        83  -5
1       106   4
-1      119    -2
-3     99     0
-5    711      4
-7   59       -4
-9  27        5
-11 15         -4
-13 2          2
-151           -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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K11a66.gif

K11a66

K11a68.gif

K11a68