Subgroup collections controlling the homotopy type of a p -local compact group

Abstract

Let (S,F,L) be a p-local compact group. We prove that the (uncompleted) homotopy type of the nerve of the linking system L is determined by the collection of subgroups of S that are F-centric and F-radical. This generalizes work of Broto, Grodal, Levi, Oliver, and the second author, who prove an analogous result for p-local finite groups.