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.
| Original language | English |
|---|---|
| Pages (from-to) | 1225-1275 |
| Number of pages | 51 |
| Journal | Algebraic and Geometric Topology |
| Volume | 24 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2024 |
Bibliographical note
Publisher Copyright:© 2024 MSP (Mathematical Sciences Publishers).
Funding
During the revision process of this work, Guillou was partially supported by Simons Collaboration Grant 282316 and NSF grants DMS-1710379 and DMS-2003204.
| Funders | Funder number |
|---|---|
| Simons Collaboration | 282316 |
| National Science Foundation Arctic Social Science Program | DMS-2003204, DMS-1710379 |
Keywords
- Atiyah duality
- G–spectra
- equivariant stable homotopy theory
- spectral Mackey functor
ASJC Scopus subject areas
- Geometry and Topology
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