Research Seminars @ Illinois

Abstract: Bordered Heegaard Floer homology is a suite of ($A_\infty$-) module-valued invariants of compact orientable 3-manifolds (with parametrized boundary) equipped with several pairing theorems, due to Lipshitz—Ozsváth--Thurston, which tell us how to recover the invariant for a 3-manifold obtained by gluing two along a shared boundary component. In the empty boundary case, Heegaard Floer homology, these invariants are known to be functorial. In this talk, which is based on joint work in progress with Gary Guth and Sungkyung Kang, we will address functoriality in the non-empty boundary case, as well as a pairing theorem for morphisms, and sketch an application.