Composition, DG-Modules, and Cobordism Maps in Bordered Floer Homology

Explore the intricacies of bordered Floer homology in this 45-minute lecture from the Western Hemisphere Virtual Symplectic Seminar. Delve into the algebraic aspects of 3-manifolds with connected boundaries, focusing on the dg-module CFD(Y). Examine the pairing theorem by Lipshitz–Ozsváth–Thurston, which establishes a homotopy equivalence between the complex of module homomorphisms and the Heegaard Floer complex. Investigate the topological interpretation of composition of module homomorphisms as maps induced by pair of pants cobordisms on Heegaard Floer complexes. Gain insights into the consequences of this interpretation and its implications for the field of symplectic geometry and topology.