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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
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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