Models of G–spectra as presheaves of spectra

Guillou, Bertrand J; May, J Peter

doi:10.2140/agt.2024.24.1225

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Models of $G$–spectra as presheaves of spectra

Bertrand J Guillou and J Peter May

Algebraic & Geometric Topology 24 (2024) 1225–1275

DOI: 10.2140/agt.2024.24.1225

Abstract

Let $G$ be a finite group. We give Quillen equivalent models for the category of $G$ –spectra as categories of spectrally enriched functors from explicitly described domain categories to nonequivariant spectra. Our preferred model is based on equivariant infinite loop space theory applied to elementary categorical data. It recasts equivariant stable homotopy theory in terms of point–set-level categories of $G$ –spans and nonequivariant spectra. We also give a more topologically grounded model based on equivariant Atiyah duality.

Keywords

equivariant stable homotopy theory, spectral Mackey functor, $G$–spectra, Atiyah duality

Mathematical Subject Classification 2010

Primary: 55P42, 55P91, 55P92

Secondary: 55P48

References

Publication

Received: 8 July 2018

Revised: 13 April 2022

Accepted: 20 November 2022

Published: 28 June 2024

Authors

Bertrand J Guillou
Department of Mathematics University of Kentucky Lexington, KY United States

J Peter May
Department of Mathematics The University of Chicago Chicago, IL United States

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Volume 24, issue 3 (2024)