Torus and Z/p actions on manifolds

Let G be either a finite cyclic group of prime order or S1. We show that if G acts on a manifold or, more generally, on a Poincaré duality space M, then each term of the Leray spectral sequence of the map M×GEG→BG satisfies a properly defined “Poincaré duality”. As a consequence of this fact we obtain new results relating the cohomology groups of M and MG. We apply our results to study group actions on 3-manifolds.