L9a21

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L9a20.gif

L9a20

L9a22.gif

L9a22

L9a21.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L9a21 at Knotilus!

L9a21 is in the Rolfsen table of links.


Link Presentations

[edit Notes on L9a21's Link Presentations]

Planar diagram presentation X8192 X2,9,3,10 X10,3,11,4 X14,8,15,7 X18,14,7,13 X6,17,1,18 X16,11,17,12 X12,6,13,5 X4,16,5,15
Gauss code {1, -2, 3, -9, 8, -6}, {4, -1, 2, -3, 7, -8, 5, -4, 9, -7, 6, -5}
A Braid Representative {{{braid_table}}}
A Morse Link Presentation L9a21 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature -1 (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 \
-5-4-3-2-101234χ
8         11
6        2 -2
4       31 2
2      42  -2
0     53   2
-2    45    1
-4   44     0
-6  25      3
-8 13       -2
-10 2        2
-121         -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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L9a20.gif

L9a20

L9a22.gif

L9a22