Alejandro Adem and Jeff Smith
Periodic complexes and group actions

Abstract: In this paper we show that the cohomology of a connected CW complex 
is periodic if and only if it is the base space of an orientable spherical 
fibration with total space that is homotopically finite dimensional. As 
applications we characterize those discrete groups that act freely and 
properly on a cartesian product of euclidean space and a sphere; we construct 
non-standard free actions of rank two simple groups on finite complexes Y 
homotopy equivalent to a product of two spheres and we prove that a finite 
p-group P acts freely on such a complex if and only if it does not contain a 
subgroup isomorphic to Z/p X Z/p X Z/p.