## Algebraic & Geometric Topology

### An algebraic model for finite loop spaces

#### Abstract

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

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

Dates
Revised: 27 February 2014
Accepted: 3 March 2014
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513716006

Digital Object Identifier
doi:10.2140/agt.2014.14.2915

Mathematical Reviews number (MathSciNet)
MR3276851

Zentralblatt MATH identifier
1306.55008

#### Citation

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. https://projecteuclid.org/euclid.agt/1513716006

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