K11a343

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K11a342.gif

K11a342

K11a344.gif

K11a344

K11a343.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

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Knot presentations

Planar diagram presentation X6271 X14,4,15,3 X16,6,17,5 X22,8,1,7 X20,10,21,9 X18,12,19,11 X4,14,5,13 X2,16,3,15 X12,18,13,17 X10,20,11,19 X8,22,9,21
Gauss code 1, -8, 2, -7, 3, -1, 4, -11, 5, -10, 6, -9, 7, -2, 8, -3, 9, -6, 10, -5, 11, -4
Dowker-Thistlethwaite code 6 14 16 22 20 18 4 2 12 10 8
A Braid Representative
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A Morse Link Presentation K11a343 ML.gif

Four dimensional invariants

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

[edit Notes for K11a343's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 31, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a343/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a343/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

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

Vassiliev invariants

V2 and V3: (8, 24)
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 K11a343. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
01234567891011χ
25           1-1
23            0
21         21 -1
19        1   1
17       22   0
15      21    1
13     22     0
11    22      0
9   12       1
7  22        0
5  1         1
312          -1
11           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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K11a342.gif

K11a342

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K11a344