K11a122

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K11a121.gif

K11a121

K11a123.gif

K11a123

K11a122.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a122 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X10,3,11,4 X14,6,15,5 X18,7,19,8 X16,9,17,10 X2,11,3,12 X20,13,21,14 X22,16,1,15 X8,17,9,18 X12,19,13,20 X6,21,7,22
Gauss code 1, -6, 2, -1, 3, -11, 4, -9, 5, -2, 6, -10, 7, -3, 8, -5, 9, -4, 10, -7, 11, -8
Dowker-Thistlethwaite code 4 10 14 18 16 2 20 22 8 12 6
A Braid Representative
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A Morse Link Presentation K11a122 ML.gif

Four dimensional invariants

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

[edit Notes for K11a122's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 127, -2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a122/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a122/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11a1, K11a149,}

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

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 -2 is the signature of K11a122. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-8-7-6-5-4-3-2-10123χ
5           1-1
3          3 3
1         51 -4
-1        93  6
-3       106   -4
-5      118    3
-7     910     1
-9    811      -3
-11   59       4
-13  28        -6
-15 15         4
-17 2          -2
-191           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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K11a121.gif

K11a121

K11a123.gif

K11a123