K11a262

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K11a261.gif

K11a261

K11a263.gif

K11a263

K11a262.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a262 at Knotilus!



Knot presentations

Planar diagram presentation X6271 X8394 X14,5,15,6 X16,8,17,7 X4,9,5,10 X20,11,21,12 X18,13,19,14 X2,15,3,16 X22,18,1,17 X12,19,13,20 X10,21,11,22
Gauss code 1, -8, 2, -5, 3, -1, 4, -2, 5, -11, 6, -10, 7, -3, 8, -4, 9, -7, 10, -6, 11, -9
Dowker-Thistlethwaite code 6 8 14 16 4 20 18 2 22 12 10
A Braid Representative
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A Morse Link Presentation K11a262 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:K11a262/ThurstonBennequinNumber
Hyperbolic Volume 14.8139
A-Polynomial See Data:K11a262/A-polynomial

[edit Notes for K11a262's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11a262's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 107, -2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a262/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a262/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11a10,}

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

Vassiliev invariants

V2 and V3: (-1, 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 -2 is the signature of K11a262. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-8-7-6-5-4-3-2-10123χ
5           1-1
3          3 3
1         41 -3
-1        83  5
-3       85   -3
-5      97    2
-7     88     0
-9    69      -3
-11   48       4
-13  26        -4
-15 14         3
-17 2          -2
-191           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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K11a261.gif

K11a261

K11a263.gif

K11a263