Volume 11, issue 1 (2007)

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

Carles Broto, Ran Levi and Bob Oliver

Geometry & Topology 11 (2007) 315–427

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”.

classifying space, $p$–completion, fusion, compact Lie groups, $p$–compact groups
Mathematical Subject Classification 2000
Primary: 55R35
Secondary: 55R40, 57T10
Forward citations
Received: 19 July 2006
Accepted: 20 November 2006
Published: 16 March 2007
Proposed: Bill Dwyer
Seconded: Haynes Miller, Paul Goerss
Carles Broto
Departament de Matemàtiques
Universitat Autònoma de Barcelona
E–08193 Bellaterra
Ran Levi
Department of Mathematical Sciences
University of Aberdeen
Meston Building 339
Aberdeen AB24 3UE
Bob Oliver
Institut Galilée
Av J-B Clément
93430 Villetaneuse