Geometry & Topology seminar

Eric Harper, McMaster University

Akbulut corks and non-trivial involutions on instanton Floer homology”

We consider a certain family of compact and contractible 4-manifolds, called corks, recently constructed by Akbulut and Yasui. Each cork Wn gives rise to exotic structures on smooth 4-manifolds via an involution of their boundary integral homology 3-sphere. The cork W1, also known as Akbulut’s cork, and its boundary involution was the first example of a diffeomorphism acting non-trivially on the instanton Floer homology of an irreducible homology 3-sphere. In this talk, we will show that each cork Wn has a diffeomorphism on the boundary that acts non-trivially on the Floer homology.