Discrete models for the p-local homotopy theory of compact Lie groups and p-compact groups

Abstract

We define and study a certain class of spaces which includes p-completed classifying spaces of compact Lie groups, classifying spaces of p-compact groups, and p-completed classifying spaces of certain locally finite discrete groups. These spaces are determined by fusion and linking systems over "discrete p-toral groups" - extensions of (ℤ/p ∞)r by finite p-groups - in the same way that classifying spaces of p-local finite groups as defined in our paper [7] are determined by fusion and linking systems over finite p-groups. We call these structures "p-local compact groups".