Algebra/Topology seminar

Speaker: Dominik Kirstein

Title: Equivariant Poincaré duality and fixed point methods

Abstract: Poincaré duality captures the homological properties of closed manifolds, and spaces satsifying Poincaré duality play a key role in their classification, for example in surgery theory. In this talk, I will present an equivariant generalisation to spaces with an action by a compact Lie group G, capturing homological properties of smooth closed G-manifolds.
As an application, I will explain how this theory can be used to give new proofs of some classical rigidity results for fixed points of group actions on manifolds and connect it to the construction of group actions on aspherical manifolds. This is based on joint work with Kaif Hilman and Christian Kremer.