In-Person and Online Talk 

In its simplest incarnation, bordered Floer homology associates to a 3-manifold Y with connected boundary an algebraic object CFD(Y) which can be regarded as a dg-module. A pairing theorem of Lipshitz–Ozsváth–Thurston tells us that the complex Mor(CFD(Y_1),CFD(Y_2)) of module homomorphisms between two of these modules is homotopy equivalent to the Heegaard Floer complex of the manifold Y obtained by gluing -Y_1 and Y_2 along their common boundary. In this talk, we will discuss a topological interpretation of composition of such module homomorphisms as the map induced on Heegaard Floer complexes by a pair of pants cobordism and some consequences of this interpretation