Geometry & Topology

Equivariant homotopy theory for pro–spectra

Halvard Fausk

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

equivariant homotopy pro-spectra profinite groups


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

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