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Gæsteforelæsning Seminar

19.02.2024   kl. 15:00 - 16:00

QM Research Seminar: Bordered Floer homology, composition, and Khovanov's arc algebras

Speaker: Jesse Cohen (University of Hamburg)


Abstract:

Bordered Floer homology, due to Lipshitz, Ozsváth, and Thurston [LOT], is a generalization of Heegaard Floer homology to 3-manifolds with parametrized boundary. The simplest incarnation of this invariant can be regarded as a differential module CFD(Y) and a pairing theorem of [LOT] tells us that the complex of module homomorphisms between two such modules is homotopy equivalent to the Heegaard Floer complex of the 3-manifold obtained by gluing. We will discuss a topological interpretation of composition of module homomorphisms in this context, and applications thereof, including forthcoming work on deformations of arc algebras and a spectral sequence for links in S^1xS^2.