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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 |
Abstract |
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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 (Z ∕ 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”. |
Keywordsclassifying space, p–completion, fusion, compact Lie groups, p–compact groups |
Mathematical Subject ClassificationPrimary: 55R35 Secondary: 55R40, 57T10 |
References |
Forward citations |
PublicationReceived: 19 July 2006 |
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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