K11n103

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K11n102.gif

K11n102

K11n104.gif

K11n104

K11n103.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 X14,5,15,6 X12,8,13,7 X9,20,10,21 X2,11,3,12 X16,13,17,14 X6,15,7,16 X17,22,18,1 X19,8,20,9 X21,18,22,19
Gauss code 1, -6, 2, -1, 3, -8, 4, 10, -5, -2, 6, -4, 7, -3, 8, -7, -9, 11, -10, 5, -11, 9
Dowker-Thistlethwaite code 4 10 14 12 -20 2 16 6 -22 -8 -18
A Braid Representative
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A Morse Link Presentation K11n103 ML.gif

Four dimensional invariants

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

[edit Notes for K11n103's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 65, -4 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11n103/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n103/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11n10, K11n144,}

Same Jones Polynomial (up to mirroring, ): {K11n175,}

Vassiliev invariants

V2 and V3: (4, -9)
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 K11n103. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-7-6-5-4-3-2-1012χ
1         11
-1        2 -2
-3       41 3
-5      53  -2
-7     63   3
-9    55    0
-11   56     -1
-13  35      2
-15 25       -3
-17 3        3
-192         -2
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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K11n102.gif

K11n102

K11n104.gif

K11n104