Link Splice Base

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

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

File:Link Splice Base.gif (Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit Data:Link Splice Base/KnotilusGaussCode Link Splice Base at Knotilus!

Link Presentations

[edit Notes on Link Splice Base's Link Presentations]

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

A Braid Representative	<* BraidPlot[CollapseBraid[BR[K]], Mode -> "Wiki", Images -> {"BraidPart0.gif", "BraidPart1.gif", "BraidPart2.gif", "BraidPart3.gif", "BraidPart4.gif"}] *>
A Morse Link Presentation	File:Link Splice Base ML.gif

Polynomial invariants

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

Data:Link Splice Base/KhovanovTable

Integral Khovanov Homology (db, data source)

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