K11a340

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K11a339.gif

K11a339

K11a341.gif

K11a341

K11a340.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a340 at Knotilus!



Knot presentations

Planar diagram presentation X6271 X14,4,15,3 X16,6,17,5 X20,8,21,7 X22,10,1,9 X18,12,19,11 X4,14,5,13 X2,16,3,15 X10,18,11,17 X12,20,13,19 X8,22,9,21
Gauss code 1, -8, 2, -7, 3, -1, 4, -11, 5, -9, 6, -10, 7, -2, 8, -3, 9, -6, 10, -4, 11, -5
Dowker-Thistlethwaite code 6 14 16 20 22 18 4 2 10 12 8
A Braid Representative
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A Morse Link Presentation K11a340 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:K11a340/ThurstonBennequinNumber
Hyperbolic Volume 12.9962
A-Polynomial See Data:K11a340/A-polynomial

[edit Notes for K11a340's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
Rasmussen s-Invariant -6

[edit Notes for K11a340's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 87, 6 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a340/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a340/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

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

Vassiliev invariants

V2 and V3: (10, 30)
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 6 is the signature of K11a340. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
01234567891011χ
29           1-1
27          2 2
25         41 -3
23        52  3
21       84   -4
19      65    1
17     78     1
15    56      -1
13   37       4
11  25        -3
9  3         3
712          -1
51           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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K11a339.gif

K11a339

K11a341.gif

K11a341