K11a331

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K11a330.gif

K11a330

K11a332.gif

K11a332

K11a331.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a331 at Knotilus!



Knot presentations

Planar diagram presentation X6271 X12,4,13,3 X18,5,19,6 X22,8,1,7 X16,9,17,10 X4,12,5,11 X20,13,21,14 X10,15,11,16 X8,17,9,18 X2,19,3,20 X14,21,15,22
Gauss code 1, -10, 2, -6, 3, -1, 4, -9, 5, -8, 6, -2, 7, -11, 8, -5, 9, -3, 10, -7, 11, -4
Dowker-Thistlethwaite code 6 12 18 22 16 4 20 10 8 2 14
A Braid Representative
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A Morse Link Presentation K11a331 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:K11a331/ThurstonBennequinNumber
Hyperbolic Volume 16.0068
A-Polynomial See Data:K11a331/A-polynomial

[edit Notes for K11a331's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11a331's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 115, -2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a331/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a331/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {10_121, K11a41, K11a183, K11a198,}

Same Jones Polynomial (up to mirroring, ): {K11a3, K11a51,}

Vassiliev invariants

V2 and V3: (1, -4)
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 K11a331. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-7-6-5-4-3-2-101234χ
7           11
5          2 -2
3         51 4
1        72  -5
-1       95   4
-3      108    -2
-5     98     1
-7    710      3
-9   59       -4
-11  27        5
-13 15         -4
-15 2          2
-171           -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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K11a330.gif

K11a330

K11a332.gif

K11a332