Georgia Institute of Technology College of Sciences

Khovanov homology is a powerful and computable homology theory for links which extends to tangles and tangle cobordisms. It is closely, but perhaps mysteriously, related to many flavors of Floer homology. Szabó has constructed a combinatorial spectral sequence from Khovanov homology which (conjecturally) converges to a Heegaard Floer-theoretic object. We will discuss work in progress to extend Szabó’s construction to an invariant of tangles and surfaces in the four-sphere.