Free actions on spaces with nonzero euler characteristic

Abstract

We use group representation theory to study free actions by finite groups on spaces with nonzero Euler characteristic. The main results are: (i) a sharp lower bound on the dimension of QH *( X; ℚ) if X is a finite CW-complex with nonzero Euler characteristic admitting a free action by a finite Abelian group and (ii) an algebraic characterization of the finite groups that can act freely on an arbitrary product of complex projective spaces (with the surprising conclusion that any such group must be a 2-group).