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.