On Khovanov homology and sutured Floer homology

On Khovanov homology and sutured Floer homology

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Elisenda Grigsby, Columbia University
Fine Hall 214

The relationship between Khovanov- and Heegaard Floer-type homology invariants is intriguing and still poorly-understood. In this talk, I will describe a connection between Khovanov's categorification of the reduced $n$-colored Jones polynomial and sutured Floer homology, a relative version of Heegaard Floer homology developed by Andras Juhasz. As a corollary, we will prove that Khovanov's categorification detects the unknot when $n>1$. This is joint work with Stephan Wehrli.