On Nielsen realization and manifold models for classifying spaces

Abstract

We consider the problem of whether, for a given virtually torsionfree discrete group Γ \Gamma , there exists a cocompact proper topological Γ \Gamma -manifold, which is equivariantly homotopy equivalent to the classifying space for proper actions. This problem is related to Nielsen Realization. We will make the assumption that the expected manifold model has a zero-dimensional singular set. Then we solve the problem in the case, for instance, that Γ \Gamma contains a normal torsionfree subgroup π \pi such that π \pi is hyperbolic and π \pi is the fundamental group of an aspherical closed manifold of dimension greater or equal to five and Γ / π \Gamma /\pi is a finite cyclic group of odd order.