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 $Y_p^{\wedge }$. 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 $p$.