ANY FINITE GROUP ACTS FREELY AND HOMOLOGICALLY TRIVIALLY ON A PRODUCT OF SPHERES

The main theorem states that if K is a finite CW-complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X x S-n for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial, then so is the action on X x S-n. Unlu and Yalcin recently showed that any finite group acts freely, cellularly, and homologicially trivially on a finite CW-complex which has the homotopy type of a product of spheres. Thus every finite group acts smoothly, freely, and homologically trivially on a product of spheres.