#### Volume 20, issue 4 (2020)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
A structure theorem for $\mathit{RO}(C_2)$–graded Bredon cohomology

### Clover May

Algebraic & Geometric Topology 20 (2020) 1691–1728
##### Abstract

Let ${C}_{2}$ be the cyclic group of order two. We present a structure theorem for the $\mathit{RO}\left({C}_{2}\right)$–graded Bredon cohomology of ${C}_{2}$–spaces using coefficients in the constant Mackey functor $\underset{¯}{{\mathbb{𝔽}}_{2}}$. We show that, as a module over the cohomology of the point, the $\mathit{RO}\left({C}_{2}\right)$–graded cohomology of a finite ${C}_{2}$–CW complex decomposes as a direct sum of two basic pieces: shifted copies of the cohomology of a point and shifted copies of the cohomologies of spheres with the antipodal action. The shifts are by elements of $\mathit{RO}\left({C}_{2}\right)$ corresponding to actual (ie nonvirtual) ${C}_{2}$–representations. This decomposition lifts to a splitting of genuine ${C}_{2}$–spectra.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/agt

We have not been able to recognize your IP address 3.237.66.86 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.

equivariant cohomology, equivariant homotopy, Toda bracket, Mackey functor, $\mathit{RO}(G)$–graded