Groups Which Act on S n Without Fixed Point

TLDR

Abstract

An equivalent formulation of the problem is the following. Which groups can occur as the fundamental groups of manifolds Mn for which the universal covering space A?n is homeomorphic to Sn. More generally one might only require that Mn have the homotopy type of S?L. (Such manifolds are classified up to homotopy type by the fundamental group together with the k-invariant (see Olum [3] Theorem IV.)) For example, any 3-manifold with a finite fundamental group satisfies this more general condition. The author is indebted to helpful discussions with A. Shapiro.