Fast Khovanov Homology Computations

Abstract

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.

12 pages, many figures. Dedicated to Lou Kauffman on his 60th birthday

References in corpus (1)

• Khovanov's homology for tangles and cobordisms

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• Khovanov homology and rational unknotting
• A computation in Khovanov-Rozansky Homology
• A binary operation on the class of coherently diagonal complexes