L9n27

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L9n26.gif

L9n26

L9n28.gif

L9n28

L9n27.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L9n27 at Knotilus!

L9n27 is in the Rolfsen table of links.


Link Presentations

[edit Notes on L9n27's Link Presentations]

Planar diagram presentation X6172 X12,7,13,8 X4,13,1,14 X9,18,10,15 X8493 X5,17,6,16 X17,5,18,14 X15,10,16,11 X2,12,3,11
Gauss code {1, -9, 5, -3}, {-8, 6, -7, 4}, {-6, -1, 2, -5, -4, 8, 9, -2, 3, 7}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gif
BraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart3.gifBraidPart2.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart0.gif
A Morse Link Presentation L9n27 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) 0 (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
7         11
5          0
3       11 0
1     31   2
-1    141   2
-3   112    2
-5   1      1
-7 111      1
-9          0
-111         -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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L9n26.gif

L9n26

L9n28.gif

L9n28