Dror Bar-Natan:
Odds, Ends, Unfinished:
# Some Khovanov-Rozansky Computations

## (as of December 2004)

For several reasons I believe the Khovanov-Rozansky homology theory for
knots (see arXiv:math.QA/0401268)
is one of the most exciting recent developments in knot theory, and
very likely also out of knot theory. But I am failing miserably on
understanding what it is. So just to verify that I understand the
definitions correctly I wrote some programs to compute some
Khovanov-Rozansky homologies.
My programs are admittedly pathetic. They are inelegant and
inefficient and they hardly compute anything. Even the trefoil knot
seems too large for these programs. (Though what's computed is enough
to convince me that I do understand the definitions, and may already be
of some very minor interest to others). Nothing was checked too
carefully and all may be wrong.

My conventions follow the Khovanov-Rozansky paper and my own one
page summary KRC.pdf.

The mathematica notebook KhovanovRozansky.nb (also available as
KhovanovRozansky.pdf) contains
pretty much all that I have computed.

If you want to re-run my computations, you need to have the packages
KnotTheory`,
SubQuotient.m and KRH.m
on your mathematica path. Use them as in the notebook KhovanovRozansky.nb.

At the moment I have no plans of trying to improve my programs.