K11a198

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K11a197.gif

K11a197

K11a199.gif

K11a199

K11a198.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

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Knot presentations

Planar diagram presentation X4251 X12,4,13,3 X16,5,17,6 X14,7,15,8 X18,10,19,9 X2,12,3,11 X22,13,1,14 X6,15,7,16 X20,18,21,17 X10,20,11,19 X8,21,9,22
Gauss code 1, -6, 2, -1, 3, -8, 4, -11, 5, -10, 6, -2, 7, -4, 8, -3, 9, -5, 10, -9, 11, -7
Dowker-Thistlethwaite code 4 12 16 14 18 2 22 6 20 10 8
A Braid Representative
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A Morse Link Presentation K11a198 ML.gif

Four dimensional invariants

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

[edit Notes for K11a198's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 115, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a198/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a198/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {10_121, K11a41, K11a183, K11a331,}

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

Vassiliev invariants

V2 and V3: (1, 0)
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 K11a198. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-5-4-3-2-10123456χ
15           11
13          3 -3
11         51 4
9        83  -5
7       95   4
5      98    -1
3     99     0
1    710      3
-1   48       -4
-3  27        5
-5 14         -3
-7 2          2
-91           -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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K11a197.gif

K11a197

K11a199.gif

K11a199