K11a241

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K11a240.gif

K11a240

K11a242.gif

K11a242

K11a241.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a241 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X14,4,15,3 X18,6,19,5 X20,8,21,7 X22,10,1,9 X16,12,17,11 X2,14,3,13 X10,16,11,15 X12,18,13,17 X8,20,9,19 X6,22,7,21
Gauss code 1, -7, 2, -1, 3, -11, 4, -10, 5, -8, 6, -9, 7, -2, 8, -6, 9, -3, 10, -4, 11, -5
Dowker-Thistlethwaite code 4 14 18 20 22 16 2 10 12 8 6
A Braid Representative
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A Morse Link Presentation K11a241 ML.gif

Four dimensional invariants

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

[edit Notes for K11a241's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 95, 6 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a241/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a241/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11a186,}

Same Jones Polynomial (up to mirroring, ): {K11a186,}

Vassiliev invariants

V2 and V3: (8, 22)
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 K11a241. 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        62  4
21       84   -4
19      76    1
17     88     0
15    57      -2
13   48       4
11  25        -3
9  4         4
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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K11a240.gif

K11a240

K11a242.gif

K11a242