PROJECTIVE-RESOLUTIONS AND POINCARE-DUALITY COMPLEXES

Let k be a field lof characteristic p > 0 and let G be a finite group. We investigate the structure of the cohomology ring H(G, k) in relat ion to certain spectral sequences determined by systems of homogeneous parameters for the cohomology ring. Each system of homogeneous parame ters is associated to a complex of projective kG-modules which is homo topically equivalent to a Poincare duality complex. The initial differ entials in the hypercohomology spectral sequence of the complex are mu ltiplications by the parameters, while the higher differentials are ma tric Massey products. If the cohomology ring is Cohen-Macaulay, then t he duality of the complex assures that the Poincare series for the coh omology satisfies a certain functional equation. The structure of the complex also implies the existence of cohomology classes which are in relatively large degrees but are not in the ideal generated by the par ameters. We consider several other questions concerned with the minima l projective resolutions and the convergence of the spectral sequence.