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Revision as of 06:59, 26 May 2009

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L2a1.gif

L2a1

L4a1.gif

L4a1

L2a1.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L2a1 at Knotilus!

L2a1 is in Rolfsen's table of links. It is also known as the "Hopf Link".

The sheet bend of practical knot tying deforms to the Hopf link.


Japanese family emblem
Linked hearts
expanded Kolam Two-hearts [1]
Logo
In Star of David form on old Jewish building in Prague
Three wreaths linked as two L2a1 configurations on Michelangelo's tomb
One form of a heterosexuality symbol
(pseudo-3D)
Are they forever linked? [2]
As impossible object
Linked hearts (pseudo-3D)
German coat of arms

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 \
-2-10χ
0  11
-2  11
-41  1
-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.

L2a1.gif

L2a1

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L4a1