L8a18

From Knot Atlas
Jump to navigationJump to search

L8a17.gif

L8a17

L8a19.gif

L8a19

L8a18.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L8a18 at Knotilus!

L8a18 is in the Rolfsen table of links.


Link Presentations

[edit Notes on L8a18's Link Presentations]

Planar diagram presentation X6172 X12,4,13,3 X8,16,9,15 X14,8,15,7 X16,10,11,9 X10,12,5,11 X2536 X4,14,1,13
Gauss code {1, -7, 2, -8}, {7, -1, 4, -3, 5, -6}, {6, -2, 8, -4, 3, -5}
A Braid Representative {{{braid_table}}}
A Morse Link Presentation L8a18 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature 4 (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 \
-2-10123456χ
17        11
15       21-1
13      1  1
11     22  0
9    21   1
7   13    2
5  21     1
3 13      2
1         0
-11        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).

Back to the top.

L8a17.gif

L8a17

L8a19.gif

L8a19