Geometry & Topology

Discrete models for the $p$–local homotopy theory of compact Lie groups and $p$–compact groups

Carles Broto, Ran Levi, and Bob Oliver

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Abstract

We define and study a certain class of spaces which includes p–completed classifying spaces of compact Lie groups, classifying spaces of p–compact groups, and p–completed classifying spaces of certain locally finite discrete groups. These spaces are determined by fusion and linking systems over “discrete p–toral groups”—extensions of (p)r by finite p–groups—in the same way that classifying spaces of p–local finite groups as defined in our paper [The homotopy theory of fusion systems, J. Amer. Math. Soc. 16 (2003) 779–856] are determined by fusion and linking systems over finite p–groups. We call these structures “p–local compact groups”.

Article information

Source
Geom. Topol., Volume 11, Number 1 (2007), 315-427.

Dates
Received: 19 July 2006
Accepted: 20 November 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799836

Digital Object Identifier
doi:10.2140/gt.2007.11.315

Mathematical Reviews number (MathSciNet)
MR2302494

Zentralblatt MATH identifier
1135.55008

Subjects
Primary: 55R35: Classifying spaces of groups and $H$-spaces
Secondary: 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20] 57T10: Homology and cohomology of Lie groups

Keywords
classifying space $p$–completion fusion compact Lie groups $p$–compact groups

Citation

Broto, Carles; Levi, Ran; Oliver, Bob. Discrete models for the $p$–local homotopy theory of compact Lie groups and $p$–compact groups. Geom. Topol. 11 (2007), no. 1, 315--427. doi:10.2140/gt.2007.11.315. https://projecteuclid.org/euclid.gt/1513799836


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