Models of G-spectra as presheaves of spectra

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.Comment: 38 pages. v4. A number of relatively small changes and corrections. The introduction has been rewritten in response to suggestions from a referee. To make this paper more self-contained, section 4 on enriched model categories of G-spectra has been added. A new section 5 addresses a minor error in the previous version