Algebraic & Geometric Topology

An algebraic model for finite loop spaces

Carles Broto, Ran Levi, and Bob Oliver

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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 Yp. 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.

Article information

Algebr. Geom. Topol., Volume 14, Number 5 (2014), 2915-2982.

Received: 13 August 2013
Revised: 27 February 2014
Accepted: 3 March 2014
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55R35: Classifying spaces of groups and $H$-spaces
Secondary: 20D20: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure 20E22: Extensions, wreath products, and other compositions [See also 20J05]

finite loop spaces classifying spaces $p$–local compact groups fusion


Broto, Carles; Levi, Ran; Oliver, Bob. An algebraic model for finite loop spaces. Algebr. Geom. Topol. 14 (2014), no. 5, 2915--2982. doi:10.2140/agt.2014.14.2915.

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