K11n82

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K11n81.gif

K11n81

K11n83.gif

K11n83

K11n82.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n82 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X8394 X5,17,6,16 X7,12,8,13 X2,9,3,10 X11,18,12,19 X13,21,14,20 X15,1,16,22 X17,10,18,11 X19,7,20,6 X21,15,22,14
Gauss code 1, -5, 2, -1, -3, 10, -4, -2, 5, 9, -6, 4, -7, 11, -8, 3, -9, 6, -10, 7, -11, 8
Dowker-Thistlethwaite code 4 8 -16 -12 2 -18 -20 -22 -10 -6 -14
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart1.gifBraidPart1.gif
BraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart2.gifBraidPart2.gif
A Morse Link Presentation K11n82 ML.gif

Four dimensional invariants

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

[edit Notes for K11n82's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 19, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant
The G2 invariant Data:K11n82/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

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 K11n82. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-5-4-3-2-10123χ
9        1-1
7       1 1
5      11 0
3     21  1
1    22   0
-1   11    0
-3  12     1
-5 11      0
-7 1       1
-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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K11n81.gif

K11n81

K11n83.gif

K11n83