Template:Link Page

[[Image:Data:Link Page/Previous Knot.gif|80px|link=Data:Link Page/Previous Knot]] [[Data:Link Page/Previous Knot]]

[[Image:Data:Link Page/Next Knot.gif|80px|link=Data:Link Page/Next Knot]] [[Data:Link Page/Next Knot]]

File:Link Page.gif (Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit Link Page at Knotilus!

Link Presentations

[edit Notes on Link Page's Link Presentations]

Planar diagram presentation	Data:Link Page/PD Presentation
Gauss code	Data:Link Page/Gauss Code

A Braid Representative	{{{braid_table}}}
A Morse Link Presentation	File:Link Page ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in [math]\displaystyle{ u }[/math], [math]\displaystyle{ v }[/math], [math]\displaystyle{ w }[/math], ...)	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 [math]\displaystyle{ t^rq^j }[/math] are shown, along with their alternating sums [math]\displaystyle{ \chi }[/math] (fixed [math]\displaystyle{ j }[/math], alternation over [math]\displaystyle{ r }[/math]). The squares with yellow highlighting are those on the "critical diagonals", where [math]\displaystyle{ j-2r=s+1 }[/math] or [math]\displaystyle{ j-2r=s-1 }[/math], where [math]\displaystyle{ s= }[/math]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.

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.

[[Image:Data:Link Page/Previous Knot.gif|80px|link=Data:Link Page/Previous Knot]] [[Data:Link Page/Previous Knot]] [[Image:Data:Link Page/Next Knot.gif|80px|link=Data:Link Page/Next Knot]] [[Data:Link Page/Next Knot]]