A homological approach to problems of compact group actions

Speaker: William Browder. Lecture 1.

Abstract: We recall the definitons of cohomology of groups and some general properties of G-spaces to give elementary proofs of the classic theorems of Smith on p-groups acting on spheres, as well as Carlsson' s generalization to free actions on products of spheres of the same dimension. The Borel constrution which transforms any G-space X into a free G-space X is used to define the H*(G) structure, and to define the Cartan-Leray specral sequence.