Algebraic & Geometric Topology

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

Magdalena Kędziorek

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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.

Article information

Algebr. Geom. Topol., Volume 17, Number 5 (2017), 3095-3136.

Received: 28 November 2016
Revised: 23 March 2017
Accepted: 6 April 2017
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55N91: Equivariant homology and cohomology [See also 19L47] 55P42: Stable homotopy theory, spectra 55P60: Localization and completion

equivariant spectra model categories algebraic model


Kędziorek, Magdalena. An algebraic model for rational $\mathrm{SO}(3)$–spectra. Algebr. Geom. Topol. 17 (2017), no. 5, 3095--3136. doi:10.2140/agt.2017.17.3095.

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