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An algebraic model for finite loop spaces

Carles Broto, Ran Levi and Bob Oliver

Algebraic & Geometric Topology 14 (2014) 2915–2982

A p–local compact group consists of a discrete p–toral group S, together with a fusion system and a linking system over S which define a classifying space having very nice homotopy properties. We prove here that if some finite regular cover of a space Y is the classifying space of a p–local compact group, then so is Y p. 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 p–local compact group at each prime p.

finite loop spaces, classifying spaces, $p$–local compact groups, fusion
Mathematical Subject Classification 2010
Primary: 55R35
Secondary: 20D20, 20E22
Received: 13 August 2013
Revised: 27 February 2014
Accepted: 3 March 2014
Published: 5 November 2014
Carles Broto
Departament de Matemàtiques
Universitat Autònoma de Barcelona
E–08193 Bellaterra
Ran Levi
Institute of Mathematics
University of Aberdeen
Fraser Noble Building 138
Aberdeen AB24 3UE
Bob Oliver
Sorbonne Paris Cité, LAGA, UMR 7539 du CNRS
Université Paris 13
99, Avenue J-B Clément
93430 Villetaneuse