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2020 A structure theorem for $\mathit{RO}(C_2)$–graded Bredon cohomology
Clover May
Algebr. Geom. Topol. 20(4): 1691-1728 (2020). DOI: 10.2140/agt.2020.20.1691

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.

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Clover May. "A structure theorem for $\mathit{RO}(C_2)$–graded Bredon cohomology." Algebr. Geom. Topol. 20 (4) 1691 - 1728, 2020. https://doi.org/10.2140/agt.2020.20.1691

Information

Received: 12 June 2018; Revised: 15 August 2019; Accepted: 26 September 2019; Published: 2020
First available in Project Euclid: 1 August 2020

zbMATH: 07226703
MathSciNet: MR4127082
Digital Object Identifier: 10.2140/agt.2020.20.1691

Subjects:
Primary: 55N91

Rights: Copyright © 2020 Mathematical Sciences Publishers

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