K11a165

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K11a164.gif

K11a164

K11a166.gif

K11a166

K11a165.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a165 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X10,4,11,3 X18,6,19,5 X16,8,17,7 X2,10,3,9 X20,11,21,12 X22,13,1,14 X8,16,9,15 X6,18,7,17 X14,19,15,20 X12,21,13,22
Gauss code 1, -5, 2, -1, 3, -9, 4, -8, 5, -2, 6, -11, 7, -10, 8, -4, 9, -3, 10, -6, 11, -7
Dowker-Thistlethwaite code 4 10 18 16 2 20 22 8 6 14 12
A Braid Representative
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A Morse Link Presentation K11a165 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11a165/ThurstonBennequinNumber
Hyperbolic Volume 12.5729
A-Polynomial See Data:K11a165/A-polynomial

[edit Notes for K11a165's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11a165's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 81, 0 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a165/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a165/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {10_87, 10_98, K11a58, K11n72,}

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

Vassiliev invariants

V2 and V3: (0, 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 K11a165. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-4-3-2-101234567χ
15           1-1
13          1 1
11         31 -2
9        51  4
7       53   -2
5      75    2
3     65     -1
1    67      -1
-1   47       3
-3  25        -3
-5 14         3
-7 2          -2
-91           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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K11a164.gif

K11a164

K11a166.gif

K11a166