K11n162

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K11n161.gif

K11n161

K11n163.gif

K11n163

K11n162.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

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Knot presentations

Planar diagram presentation X6271 X3,11,4,10 X12,6,13,5 X22,8,1,7 X16,10,17,9 X11,19,12,18 X8,14,9,13 X20,16,21,15 X17,4,18,5 X2,19,3,20 X14,22,15,21
Gauss code 1, -10, -2, 9, 3, -1, 4, -7, 5, 2, -6, -3, 7, -11, 8, -5, -9, 6, 10, -8, 11, -4
Dowker-Thistlethwaite code 6 -10 12 22 16 -18 8 20 -4 2 14
A Braid Representative
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A Morse Link Presentation K11n162 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number
3-genus 2
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11n162/ThurstonBennequinNumber
Hyperbolic Volume 13.1069
A-Polynomial See Data:K11n162/A-polynomial

[edit Notes for K11n162's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11n162's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 55, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11n162/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n162/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {9_39,}

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

Vassiliev invariants

V2 and V3: (2, 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 K11n162. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
0123456789χ
21         1-1
19        2 2
17       31 -2
15      42  2
13     53   -2
11    44    0
9   45     1
7  34      -1
5 14       3
313        -2
12         2
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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K11n161.gif

K11n161

K11n163.gif

K11n163