Symmetries and Heegaard Floer homology

Robert Lipschitz (Oregon)

Abstract: Many of the recent developments in Floer-theoretic invariants of 3- and 4-manifolds have used symmetries under finite group actions -- especially Z/2. We will start by surveying some of those kinds of symmetries and applications. Then, we will talk about three different ways of encoding Z/2 symmetries in Heegaard diagrams, briefly introduce Guth-Manolescu's real Heegaard Floer homology, and sketch an extension of it to 3-manifolds with boundary. The last part is joint work with Peter Ozsváth; there is related work by Binns-Guth-Xiao.