Commutative algebra for cohomology rings of classifying spaces of compact Lie groups

Abstract

We apply the techniques of highly structured ring and module spectra to prove a duality theorem for the cohomology ring of the classifying space of a compact Lie group. This generalizes results of Benson-Carlson [2, 3] and Greenlees [10] in the case of finite groups. In particular, we prove a functional equation for the Poincaré series in the oriented Cohen-Macaulay case.