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An algebraic model for rational toral $G$–spectra

David Barnes, John Greenlees and Magdalena Kędziorek

Algebraic & Geometric Topology 19 (2019) 3541–3599
Abstract

For G a compact Lie group, toral G–spectra are those rational G–spectra whose geometric isotropy consists of subgroups of a maximal torus of G. The homotopy category of rational toral G–spectra is a retract of the category of all rational G–spectra.

We show that the abelian category of Greenlees (Algebr. Geom. Topol. 16 (2016) 1953–2019) gives an algebraic model for the toral part of rational G–spectra. This is a major step in establishing an algebraic model for all rational G–spectra for any compact Lie group G.

Keywords
equivariant cohomology, rational equivariant spectra, algebraic models, model category
Mathematical Subject Classification 2010
Primary: 55N91
Secondary: 55P42, 55P60
References
Publication
Received: 12 June 2018
Revised: 10 January 2019
Accepted: 5 March 2019
Published: 17 December 2019
Authors
David Barnes
Mathematical Sciences Research Centre
Queen’s University Belfast
Belfast
United Kingdom
John Greenlees
Mathematics Institute
University of Warwick
Coventry
United Kingdom
Magdalena Kędziorek
Max Planck Institute for Mathematics
Bonn
Germany
Mathematical Institute
Utrecht University
Utrecht
Netherlands