Alternative stable homotopy classification of p-completed classifying spaces
Abstract
Description
We give an alternative to the stable classification of p-completed homotopy types of classifying spaces of finite groups offered by Martino-Priddy. For a finite group G with Sylow subgroup S, we regard the stable p-completed classifying space of G as an object under the stable p-completed classifying space of S via the canonical inclusion map. Thus we get a classification in terms of induced fusion systems. Applying Oliver's solution to the Martino-Priddy conjecture, we obtain the surprising result that the unstable p-completed homotopy type of BG is determined by the stable p-completed inclusion of BS in BG, but not by the stable p-completed homotopy type of BG.
10 pages. Clarified text after Definition 1.1 and altered discussion in Section 4 following suggestions from referee. To appear in Topology
10 pages. Clarified text after Definition 1.1 and altered discussion in Section 4 following suggestions from referee. To appear in Topology