L9a3

From Knot Atlas
Jump to navigationJump to search

L9a2.gif

L9a2

L9a4.gif

L9a4

L9a3.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L9a3 at Knotilus!

L9a3 is in the Rolfsen table of links.


Link Presentations

[edit Notes on L9a3's Link Presentations]

Planar diagram presentation X6172 X16,7,17,8 X4,17,1,18 X12,6,13,5 X8493 X14,10,15,9 X10,14,11,13 X18,12,5,11 X2,16,3,15
Gauss code {1, -9, 5, -3}, {4, -1, 2, -5, 6, -7, 8, -4, 7, -6, 9, -2, 3, -8}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart3.gif
BraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart1.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart2.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L9a3 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 \
-3-2-10123456χ
14         11
12        3 -3
10       31 2
8      53  -2
6     53   2
4    45    1
2   55     0
0  26      4
-2 13       -2
-4 2        2
-61         -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.

L9a2.gif

L9a2

L9a4.gif

L9a4