Geometry & Topology

Equivariant homotopy theory for pro–spectra

Halvard Fausk

Full-text: Open access

Abstract

We extend the theory of equivariant orthogonal spectra from finite groups to profinite groups, and more generally from compact Lie groups to compact Hausdorff groups. The G–homotopy theory is “pieced together” from the GU–homotopy theories for suitable quotient groups GU of G; a motivation is the way continuous group cohomology of a profinite group is built out of the cohomology of its finite quotient groups. In the model category of equivariant spectra Postnikov towers are studied from a general perspective. We introduce pro–G–spectra and construct various model structures on them. A key property of the model structures is that pro–spectra are weakly equivalent to their Postnikov towers. We discuss two versions of a model structure with “underlying weak equivalences”. One of the versions only makes sense for pro–spectra. In the end we use the theory to study homotopy fixed points of pro–G–spectra.

Article information

Source
Geom. Topol., Volume 12, Number 1 (2008), 103-176.

Dates
Received: 20 December 2006
Revised: 16 April 2007
Accepted: 23 July 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800016

Digital Object Identifier
doi:10.2140/gt.2008.12.103

Mathematical Reviews number (MathSciNet)
MR2377247

Zentralblatt MATH identifier
1135.55005

Subjects
Primary: 55P91: Equivariant homotopy theory [See also 19L47]
Secondary: 18G55: Homotopical algebra

Keywords
equivariant homotopy pro-spectra profinite groups

Citation

Fausk, Halvard. Equivariant homotopy theory for pro–spectra. Geom. Topol. 12 (2008), no. 1, 103--176. doi:10.2140/gt.2008.12.103. https://projecteuclid.org/euclid.gt/1513800016


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