Algebra/Topology seminar

Speaker: Christian Kremer

Title: Constructing group actions and equivariant Poincaré duality.

Abstract: The study of group actions on manifolds is nearly as old as geometric topology itself, and a rich array of tools has been developed to approach it. Among these, equivariant surgery has played a central role in establishing uniqueness and classification results.

In this talk, I will discuss recent joint work with Hilman and Kirstein on equivariant and isovariant Poincaré duality spaces. This framework provides a new tool for constructing G-manifolds within a given G-homotopy type. I will also outline how these methods can be applied to the Nielsen realization problem for group actions on high-dimensional aspherical manifolds.