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Khovanov homology and knot Floer homology for pointed links

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HTL - Homology theories in low dimensional topology

There are spectral sequences relating reduced Khovanov homology to a variety of other homological link invariants, including the Heegaard Floer homology of the branched double cover and instanton knot homology. However, there is no known relationship between Khovanov homology and knot Floer homology, despite considerable computational evidence and numerous formal similarities. I will describe ongoing efforts to find a spectral sequence relating these two invariants. Specifically, we construct a variant of Khovanov homology for links with one or more basepoints on each component, which more closely parallels the behavior of knot Floer homology and which conjecturally fits into a spectral sequence as required. This is joint work with John Baldwin and Sucharit Sarkar.



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