K11a114

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K11a113.gif

K11a113

K11a115.gif

K11a115

K11a114.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a114 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X10,4,11,3 X14,6,15,5 X18,7,19,8 X2,10,3,9 X16,12,17,11 X6,14,7,13 X22,16,1,15 X20,17,21,18 X8,19,9,20 X12,22,13,21
Gauss code 1, -5, 2, -1, 3, -7, 4, -10, 5, -2, 6, -11, 7, -3, 8, -6, 9, -4, 10, -9, 11, -8
Dowker-Thistlethwaite code 4 10 14 18 2 16 6 22 20 8 12
A Braid Representative {{{braid_table}}}
A Morse Link Presentation K11a114 ML.gif

Four dimensional invariants

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

[edit Notes for K11a114's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 151, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a114/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a114/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

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

Vassiliev invariants

V2 and V3: (2, 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 2 is the signature of K11a114. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-3-2-1012345678χ
19           11
17          3 -3
15         61 5
13        103  -7
11       116   5
9      1310    -3
7     1211     1
5    913      4
3   712       -5
1  310        7
-1 16         -5
-3 3          3
-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).

Back to the top.

K11a113.gif

K11a113

K11a115.gif

K11a115