An equivariant cohomological approach to Smith theory and its converse

Abstract

The present work is devoted to the study of the topological properties of the fixed point set of a group action. In particular, we will first set the foundational machinery needed to study G-spaces using equivariant cohomology. Then, we will apply this machinery to generalize the classical result of Smith theory that relates the cohomology of a space with the cohomology of the fixed points of a p-group action following a proof by P. May. Finally, we will address the converse problem studied by L.Jones: when can a space be realized as the fixed point set of a semi-free group action on a contractible space.