On the integral cohomology of wreath products

TL;DR

This paper investigates the additive structure of the integral cohomology of certain wreath product spaces, relating it to the cohomology of the underlying space X, with implications for finite group cohomology.

Contribution

It provides a new description of the integral cohomology of wreath product spaces under mild conditions, extending to related spaces and deriving corollaries for finite groups.

Findings

Additive structure of cohomology described in terms of X

Weaker results obtained for similar spaces

Corollaries for finite group cohomology

Abstract

Under mild conditions on the space X, we describe the additive structure of the integral cohomology of the space $X^p \times_{C_p}EC_p$ in terms of the cohomology of X. We give weaker results for other similar spaces, and deduce various corollaries concerning the cohomology of finite groups.