The stable free rank of symmetry of products of spheres

Abstract

A well known conjecture in the theory of transformation groups states that if p is a prime and (ℤ/p)r acts freely on a product of k spheres, then r≤k. We prove this assertion if p is large compared to the dimension of the product of spheres. The argument builds on tame homotopy theory for non-simply connected spaces. © Springer-Verlag 2009.