Cork involutions and Floer homology
Building on the algebraic framework developed by Hendricks, Manolescu, and Zemke, we introduce and study a set of Floer-theoretic invariants aimed at detecting corks. Our invariants obstruct the extension of a given involution over any homology ball, rather than a particular contractible manifold. We construct several new families of corks and show that various known families of corks satisfy this property. We also discuss connections with homology cobordism and give some applications regarding the bordism group of diffeomorphisms. This is joint work with Matthew Hedden and Abhishek Mallick.