[math/0508135] On the generalized Nielsen realization problem

[math/0508135] On the generalized Nielsen realization problem

Authors: Jonathan Block, Shmuel Weinberger
Subj-class: Geometric Topology
MSC-class: 57N

The main goal of this paper is to give the first examples of equivariant aspherical Poincare complexes, that are not realized by group actions on closed aspherical manifolds $M$. These will also provide new counterexamples to the Nielsen realization problem about lifting homotopy actions of finite groups to honest group actions. Our examples show that one cannot guarantee that a given action of a finitely generated group $\pi$ on Euclidean space extends to an action of $\Pi$, a group containing $\pi$ as a subgroup of finite index, even when all the torsion of $\Pi$ lives in $\pi$.