K11n167

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K11n166.gif

K11n166

K11n168.gif

K11n168

K11n167.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

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Knot presentations

Planar diagram presentation X6271 X10,4,11,3 X14,6,15,5 X20,8,21,7 X2,10,3,9 X11,18,12,19 X4,14,5,13 X22,15,1,16 X17,12,18,13 X8,20,9,19 X16,21,17,22
Gauss code 1, -5, 2, -7, 3, -1, 4, -10, 5, -2, -6, 9, 7, -3, 8, -11, -9, 6, 10, -4, 11, -8
Dowker-Thistlethwaite code 6 10 14 20 2 -18 4 22 -12 8 16
A Braid Representative
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A Morse Link Presentation K11n167 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:K11n167/ThurstonBennequinNumber
Hyperbolic Volume 14.2087
A-Polynomial See Data:K11n167/A-polynomial

[edit Notes for K11n167's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11n167's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 63, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11n167/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n167/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11n146,}

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

Vassiliev invariants

V2 and V3: (4, 7)
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 K11n167. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-2-101234567χ
17         1-1
15        2 2
13       51 -4
11      42  2
9     65   -1
7    64    2
5   36     3
3  46      -2
1 14       3
-1 3        -3
-31         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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K11n166.gif

K11n166

K11n168.gif

K11n168