On Nielsen realization and manifold models for classifying spaces
We consider the problem of whether, for a given virtually torsionfree discrete group $Γ$, there exists a cocompact proper topological $Γ$-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 $Γ$ contains a normal torsionfree subgroup $π$ such tha…