Universität Augsburg
Institut für Mathematik

In the early 20th century, Jakob Nielsen asked if every finite group action up to homotopy on a surface may be realized as an action by homeomorphisms. For example, if a surface admits a self map whose n-th power is homotopic to the identity, is it homotopic to a homeomorphism of order n? He answered this question in the positive for cyclic groups himself, and Kerckhoff gave an affirmative answer in the 80s in complete generality. Much progress has been made on generalizations from the geometric side.

In my talk, I will discuss the analogous question for high dimensional aspherical manifolds, and report on some progress, which relies on recent joint work on equivariant Poincaré duality with Kaif Hillman and Dominik Kirstein.