K11a95

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K11a94.gif

K11a94

K11a96.gif

K11a96

K11a95.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a95 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X10,4,11,3 X12,6,13,5 X18,8,19,7 X2,10,3,9 X8,12,9,11 X22,14,1,13 X20,16,21,15 X6,18,7,17 X16,20,17,19 X14,22,15,21
Gauss code 1, -5, 2, -1, 3, -9, 4, -6, 5, -2, 6, -3, 7, -11, 8, -10, 9, -4, 10, -8, 11, -7
Dowker-Thistlethwaite code 4 10 12 18 2 8 22 20 6 16 14
A Braid Representative {{{braid_table}}}
A Morse Link Presentation K11a95 ML.gif

Four dimensional invariants

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

[edit Notes for K11a95's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 73, 4 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a95/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a95/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {10_53,}

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

Vassiliev invariants

V2 and V3: (6, 15)
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 4 is the signature of K11a95. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
01234567891011χ
27           1-1
25          2 2
23         31 -2
21        42  2
19       63   -3
17      54    1
15     66     0
13    45      -1
11   36       3
9  24        -2
7  3         3
512          -1
31           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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K11a94.gif

K11a94

K11a96.gif

K11a96