Algebraic & Geometric Topology

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

Magdalena Kędziorek

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841494

Digital Object Identifier
doi:10.2140/agt.2017.17.3095

Mathematical Reviews number (MathSciNet)
MR3704254

Zentralblatt MATH identifier
1377.55005

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

Keywords
equivariant spectra model categories algebraic model

Citation

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. https://projecteuclid.org/euclid.agt/1510841494


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