Template:Link Page

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Knot presentations

Planar diagram presentation	Data:Link Page/PD Presentation
Gauss code	Data:Link Page/Gauss Code
A Braid Representative (for some knots you may need a wide browser window!)	{{{braid_table}}}
A Morse Link Presentation	File:Link Page ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...)	Data:Link Page/Multivariable Alexander (db)
Jones polynomial	Data:Link Page/Jones Polynomial (db)
Signature	Data:Link Page/Signature (db)
HOMFLY-PT polynomial	Data:Link Page/HOMFLYPT Polynomial (db)
Kauffman polynomial	Data:Link Page/Kauffman Polynomial (db)

Khovanov Homology

The coefficients of the monomials $t^{r}q^{j}$ are shown, along with their alternating sums $\chi$ (fixed $j$, alternation over $r$). The squares with yellow highlighting are those on the "critical diagonals", where $j-2r=s+1$ or $j-2r=s-1$, where $s=$Data:Link Page/Signature is the signature of Link Page. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

Data:Link Page/KhovanovTable

Integral Khovanov Homology (db, data source)

Data:Link Page/Integral Khovanov Homology

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session. {{{computer_talk}}}

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.

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