Volume 20, issue 4 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 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 C2 be the cyclic group of order two. We present a structure theorem for the RO(C2)–graded Bredon cohomology of C2–spaces using coefficients in the constant Mackey functor 𝔽2 ¯. We show that, as a module over the cohomology of the point, the RO(C2)–graded cohomology of a finite C2–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 RO(C2) corresponding to actual (ie nonvirtual) C2–representations. This decomposition lifts to a splitting of genuine C2–spectra.

Keywords
equivariant cohomology, equivariant homotopy, Toda bracket, Mackey functor, $\mathit{RO}(G)$–graded
Mathematical Subject Classification 2010
Primary: 55N91
References
Publication
Received: 12 June 2018
Revised: 15 August 2019
Accepted: 26 September 2019
Published: 20 July 2020
Authors
Clover May
Department of Mathematics
University of California, Los Angeles
Los Angeles, CA
United States