Some examples of discrete group actions on aspherical manifolds

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Description/Abstract

We construct two classes of examples of virtually torsion-free groups G acting properly cocompactly on contractible manifolds X. In the first class of examples, the universal space for proper actions has no model with finitely many orbits of cells (and so the given manifold X cannot have this equivariant homotopy type). The reason is that the centralizers of some finite subgroups of G do not have finite-type classifying spaces.

In the second class of examples, X is a CAT(0) manifold upon which G acts by isometries, and hence X is a model for the universal space for proper G actions. In these examples, the fixed-point sets for some finite subgroups of G are not manifolds and the centralizers of these subgroups are not virtual Poincare duality groups.