K11n100

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K11n99.gif

K11n99

K11n101.gif

K11n101

K11n100.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

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Knot presentations

Planar diagram presentation X4251 X10,3,11,4 X14,6,15,5 X12,8,13,7 X9,19,10,18 X2,11,3,12 X6,14,7,13 X15,22,16,1 X17,20,18,21 X19,9,20,8 X21,16,22,17
Gauss code 1, -6, 2, -1, 3, -7, 4, 10, -5, -2, 6, -4, 7, -3, -8, 11, -9, 5, -10, 9, -11, 8
Dowker-Thistlethwaite code 4 10 14 12 -18 2 6 -22 -20 -8 -16
A Braid Representative
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A Morse Link Presentation K11n100 ML.gif

Four dimensional invariants

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

[edit Notes for K11n100's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 45, 0 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11n100/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n100/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {9_37,}

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

Vassiliev invariants

V2 and V3: (-3, -3)
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 K11n100. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-3-2-10123456χ
13         11
11        1 -1
9       31 2
7      31  -2
5     43   1
3    43    -1
1   34     -1
-1  35      2
-3 12       -1
-5 3        3
-71         -1
Integral Khovanov Homology

(db, data source)

  
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{2}}

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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K11n99.gif

K11n99

K11n101.gif

K11n101