L8a11

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L8a10.gif

L8a10

L8a12.gif

L8a12

L8a11.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L8a11 at Knotilus!

L8a11 is in the Rolfsen table of links.


Link Presentations

[edit Notes on L8a11's Link Presentations]

Planar diagram presentation X8192 X2,9,3,10 X10,3,11,4 X14,5,15,6 X16,11,7,12 X12,15,13,16 X6718 X4,13,5,14
Gauss code {1, -2, 3, -8, 4, -7}, {7, -1, 2, -3, 5, -6, 8, -4, 6, -5}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gif
BraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L8a11 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature -5 (db)
HOMFLY-PT polynomial (db)
Kauffman polynomial (db)

Khovanov Homology

The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ).   
\ r
  \  
j \
-8-7-6-5-4-3-2-10χ
-4        11
-6       110
-8      2  2
-10     11  0
-12    32   1
-14   11    0
-16  23     -1
-18 12      1
-20 1       -1
-221        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 Link Page master template (intermediate).

See/edit the Link_Splice_Base (expert).

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L8a10.gif

L8a10

L8a12.gif

L8a12