L11a311

From Knot Atlas
Jump to navigationJump to search

L11a310.gif

L11a310

L11a312.gif

L11a312

L11a311.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11a311 at Knotilus!


Link Presentations

[edit Notes on L11a311's Link Presentations]

Planar diagram presentation X10,1,11,2 X12,4,13,3 X22,12,9,11 X2,9,3,10 X20,18,21,17 X18,5,19,6 X4,19,5,20 X14,7,15,8 X16,13,17,14 X8,15,1,16 X6,22,7,21
Gauss code {1, -4, 2, -7, 6, -11, 8, -10}, {4, -1, 3, -2, 9, -8, 10, -9, 5, -6, 7, -5, 11, -3}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart2.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L11a311 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 \
-7-6-5-4-3-2-101234χ
8           11
6          3 -3
4         61 5
2        93  -6
0       116   5
-2      1210    -2
-4     1110     1
-6    812      4
-8   611       -5
-10  39        6
-12 15         -4
-14 3          3
-161           -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.

L11a310.gif

L11a310

L11a312.gif

L11a312