On the generalized Nielsen realization problem

  • Jonathan Block

    University of Pennsylvania, Philadelphia, United States
  • Shmuel Weinberger

    University of Chicago, United States


The main goal of this paper is to give the first examples of equivariant aspherical Poincaré 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 π on Euclidean space extends to an action of Π, a group containing π as a subgroup of finite index, even when all the torsion of Π lives in π.

Cite this article

Jonathan Block, Shmuel Weinberger, On the generalized Nielsen realization problem. Comment. Math. Helv. 83 (2008), no. 1, pp. 21–33

DOI 10.4171/CMH/116