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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 |
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Geometry & Topology 11 (2007) 315–427
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Abstract |
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We define and study a certain class of spaces which includes –completed classifying spaces of compact Lie groups, classifying spaces of –compact groups, and –completed classifying spaces of certain locally finite discrete groups. These spaces are determined by fusion and linking systems over “discrete –toral groups”—extensions of by finite –groups—in the same way that classifying spaces of –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 –groups. We call these structures “–local compact groups”. |
Keywords
classifying space, $p$–completion, fusion, compact Lie
groups, $p$–compact groups
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Mathematical Subject Classification 2000
Primary: 55R35
Secondary: 55R40, 57T10
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References |
Forward citations |
Publication
Received: 19 July 2006
Accepted: 20 November 2006
Published: 16 March 2007
Proposed: Bill Dwyer
Seconded: Haynes Miller, Paul Goerss
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Authors |
| Carles Broto | |
| Departament de Matemàtiques Universitat Autònoma de Barcelona E–08193 Bellaterra Spain |
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| Ran Levi | |
| Department of Mathematical
Sciences University of Aberdeen Meston Building 339 Aberdeen AB24 3UE UK |
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| Bob Oliver | |
| LAGA Institut Galilée Av J-B Clément 93430 Villetaneuse France |
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