K11a141

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K11a140.gif

K11a140

K11a142.gif

K11a142

K11a141.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a141 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X10,3,11,4 X16,6,17,5 X18,7,19,8 X12,10,13,9 X2,11,3,12 X8,14,9,13 X20,15,21,16 X22,18,1,17 X14,19,15,20 X6,21,7,22
Gauss code 1, -6, 2, -1, 3, -11, 4, -7, 5, -2, 6, -5, 7, -10, 8, -3, 9, -4, 10, -8, 11, -9
Dowker-Thistlethwaite code 4 10 16 18 12 2 8 20 22 14 6
A Braid Representative
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A Morse Link Presentation K11a141 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:K11a141/ThurstonBennequinNumber
Hyperbolic Volume 14.9456
A-Polynomial See Data:K11a141/A-polynomial

[edit Notes for K11a141's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11a141's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 103, -2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a141/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a141/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11a12,}

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

Vassiliev invariants

V2 and V3: (-2, 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 K11a141. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-6-5-4-3-2-1012345χ
9           1-1
7          3 3
5         41 -3
3        73  4
1       74   -3
-1      97    2
-3     88     0
-5    68      -2
-7   48       4
-9  26        -4
-11 14         3
-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).

Back to the top.

K11a140.gif

K11a140

K11a142.gif

K11a142