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arxiv: math/0606318 · v1 · submitted 2006-06-13 · 🧮 math.GT

Fast Khovanov Homology Computations

Dror Bar-Natan This is my paper
classification 🧮 math.GT
keywords khovanovhomologyassociatedcomputationslocaltermsalgorithmcancel
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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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  1. Khovanov complexes for bipartite links

    hep-th 2026-05 unverdicted novelty 2.0

    Shows that the Kauffman-Khovanov 2²-hypercube reduces to the bipartite 3-hypercube for N=2, confirming consistency of the reduction for bipartite links.