last updated May. 20, 2007
first edition: Jun. 13, 2006.
To Lou Kauffman, who gave us .
We introduce a local algorithm for Khovanov Homology computations - that is, we explain how it is possible to "cancel" terms in the Khovanov complex associated with a ("local") tangle, hence canceling the many associated "global" terms in one swoosh early on. This leads to a dramatic improvement in computational efficiency. Thus our program can rapidly compute certain Khovanov homology groups that otherwise would have taken centuries to evaluate.
The paper. FastKh.pdf, FastKh.ps.gz, FastKh.tar.gz, arXiv:math.GT/0606318, Journal of Knot Theory and Its Ramifications, 16-3 (2007) 243-255.
Related handouts. LocalKh.pdf, ComputationsAndMutations.pdf.
Also see my earlier paper on the subject, "Khovanov's Homology for Tangles and Cobordisms".