#### Volume 14, issue 5 (2014)

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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
##### 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 ${Y}_{p}^{\wedge }$. 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 $p$.

##### Keywords
finite loop spaces, classifying spaces, $p$–local compact groups, fusion
##### Mathematical Subject Classification 2010
Primary: 55R35
Secondary: 20D20, 20E22