An algebraic model for finite loop spaces

Broto, Carles¹ ; Levi, Ran² ; Oliver, Bob³

¹Departament de Matemàtiques, Universitat Autònoma de Barcelona, E–08193 Bellaterra, Spain
²Institute of Mathematics, University of Aberdeen, Fraser Noble Building 138, Aberdeen AB24 3UE, UK
³Sorbonne Paris Cité, LAGA, UMR 7539 du CNRS, Université Paris 13, 99, Avenue J-B Clément, 93430 Villetaneuse, France

Algebraic and Geometric Topology, Tome 14 (2014) no. 5, pp. 2915-2982

Résumé

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.

Détail

DOI : 10.2140/agt.2014.14.2915

Classification : 55R35, 20D20, 20E22
Keywords: finite loop spaces, classifying spaces, $p$–local compact groups, fusion

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