K11a208

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K11a207.gif

K11a207

K11a209.gif

K11a209

K11a208.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a208 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X12,3,13,4 X16,5,17,6 X18,7,19,8 X20,9,21,10 X14,12,15,11 X2,13,3,14 X22,15,1,16 X10,17,11,18 X8,19,9,20 X6,21,7,22
Gauss code 1, -7, 2, -1, 3, -11, 4, -10, 5, -9, 6, -2, 7, -6, 8, -3, 9, -4, 10, -5, 11, -8
Dowker-Thistlethwaite code 4 12 16 18 20 14 2 22 10 8 6
A Braid Representative
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A Morse Link Presentation K11a208 ML.gif

Four dimensional invariants

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

[edit Notes for K11a208's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 105, -4 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a208/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a208/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

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

Vassiliev invariants

V2 and V3: (6, -15)
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 -4 is the signature of K11a208. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-9-8-7-6-5-4-3-2-1012χ
1           11
-1          2 -2
-3         41 3
-5        73  -4
-7       83   5
-9      87    -1
-11     98     1
-13    68      2
-15   59       -4
-17  26        4
-19 15         -4
-21 2          2
-231           -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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K11a207.gif

K11a207

K11a209.gif

K11a209