L10a4

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L10a3.gif

L10a3

L10a5.gif

L10a5

L10a4.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L10a4 at Knotilus!


Link Presentations

[edit Notes on L10a4's Link Presentations]

Planar diagram presentation X6172 X14,7,15,8 X4,15,1,16 X12,6,13,5 X8493 X16,10,17,9 X20,18,5,17 X18,11,19,12 X10,19,11,20 X2,14,3,13
Gauss code {1, -10, 5, -3}, {4, -1, 2, -5, 6, -9, 8, -4, 10, -2, 3, -6, 7, -8, 9, -7}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gif
A Morse Link Presentation L10a4 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 \
-5-4-3-2-1012345χ
12          1-1
10         3 3
8        41 -3
6       73  4
4      74   -3
2     87    1
0    79     2
-2   46      -2
-4  37       4
-6 14        -3
-8 3         3
-101          -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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L10a3.gif

L10a3

L10a5.gif

L10a5