Homotopy functoriality of the Khovanov spectrum

Associated to a link L is a stable homotopy type X(L), the Khovanov spectrum, whose singular homology is the Khovanov homology of L. The talk will start with an overview of what properties of Khovanov homology have been lifted to the Khovanov spectrum, and which are not known to lift. We will then discuss an obstruction to lifting Khovanov’s proof of functoriality of Khovanov homology (under link cobordisms), and how a modest change to his argument overcomes this obstruction. This is joint work with Tyler Lawson and Sucharit Sarkar.

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