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An algebraic model for
finite loop spaces
Carles Broto, Ran Levi and Bob Oliver |
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Algebraic & Geometric Topology 14 (2014) 2915–2982
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Abstract |
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A –local compact group consists of a discrete –toral group , together with a fusion system and a linking system over which define a classifying space having very nice homotopy properties. We prove here that if some finite regular cover of a space is the classifying space of a –local compact group, then so is . Together with earlier results by Dwyer and Wilkerson and by the authors, this implies as a special case that a finite loop space determines a –local compact group at each prime . |
Keywords
finite loop spaces, classifying spaces, $p$–local compact
groups, fusion
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Mathematical Subject Classification 2010
Primary: 55R35
Secondary: 20D20, 20E22
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References |
Publication
Received: 13 August 2013
Revised: 27 February 2014
Accepted: 3 March 2014
Published: 5 November 2014
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Authors |
| Carles Broto | |
| Departament de Matemàtiques Universitat Autònoma de Barcelona E–08193 Bellaterra Spain |
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| Ran Levi | |
| Institute of Mathematics University of Aberdeen Fraser Noble Building 138 Aberdeen AB24 3UE UK |
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| Bob Oliver | |
| Sorbonne Paris Cité, LAGA, UMR 7539
du CNRS Université Paris 13 99, Avenue J-B Clément 93430 Villetaneuse France |
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