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An algebraic model for rational $\mathrm{SO}(3)$–spectra

Magdalena Kędziorek

Algebraic & Geometric Topology 17 (2017) 3095–3136
Abstract

Greenlees established an equivalence of categories between the homotopy category of rational SO(3)–spectra and the derived category dA(SO(3)) of a certain abelian category. In this paper we lift this equivalence of homotopy categories to the level of Quillen equivalences of model categories. Methods used in this paper provide the first step towards obtaining an algebraic model for the toral part of rational G–spectra, for any compact Lie group G.

Keywords
equivariant spectra, model categories, algebraic model
Mathematical Subject Classification 2010
Primary: 55N91, 55P42, 55P60
References
Publication
Received: 28 November 2016
Revised: 23 March 2017
Accepted: 6 April 2017
Published: 19 September 2017
Authors
Magdalena Kędziorek
Max Planck Institute for Mathematics
Bonn
Germany