Discrete models for the \(p\)-local homotopy theory of compact Lie groups and \(p\)-compact groups
The \(p\)-completed classifying spaces of finite and compact Lie groups, together with classifying spaces of \(p\)-compact groups share many similar homotopy theoretic properties. Despite these similarities the techniques used to derive them are different in each case. The aim of this paper is to provide a framework in which these similar results a derived from the common framework. The key idea is to replace fusion systems over finite \(p\)-groups with fusion systems over discrete \(p\)-toral groups. A \(p\)-toral group being a group that contains a \(p\)-torus (a group of the form \(({\mathbb Z}/p^{\infty})^{r}\) for some \(r \geq 0\)) as a normal subgroup of \(p\)-power index. The fusion system describes the way in which the various subgroups of a \(p\)-toral group fit together. In developing this theory of fusions systems the authors show how to define the classifying spaces in ways that include the Lie case and the discrete group case.
scientific article; zbMATH DE number 5136063
scientific article