Fast Khovanov Homology Computations

Details Fast Khovanov Homology Computations Fast Khovanov Homology Computations

2006-06-13

arxiv.org/abs/math/0606318v1

Mathematics

Geometric Topology

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

Scientific paper

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.

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