K11a110

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K11a109.gif

K11a109

K11a111.gif

K11a111

K11a110.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a110 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X10,4,11,3 X14,5,15,6 X16,8,17,7 X2,10,3,9 X22,11,1,12 X20,13,21,14 X18,15,19,16 X6,18,7,17 X8,19,9,20 X12,21,13,22
Gauss code 1, -5, 2, -1, 3, -9, 4, -10, 5, -2, 6, -11, 7, -3, 8, -4, 9, -8, 10, -7, 11, -6
Dowker-Thistlethwaite code 4 10 14 16 2 22 20 18 6 8 12
A Braid Representative
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A Morse Link Presentation K11a110 ML.gif

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
Rasmussen s-Invariant 0

[edit Notes for K11a110's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 97, 0 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a110/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a110/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11a4,}

Same Jones Polynomial (up to mirroring, ): {K11a257,}

Vassiliev invariants

V2 and V3: (0, 2)
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 0 is the signature of K11a110. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-6-5-4-3-2-1012345χ
11           1-1
9          2 2
7         41 -3
5        62  4
3       74   -3
1      96    3
-1     78     1
-3    68      -2
-5   47       3
-7  26        -4
-9 14         3
-11 2          -2
-131           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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K11a109.gif

K11a109

K11a111.gif

K11a111