Alternative stable homotopy classification of p-completed classifying spaces

2005/02/28 by Kari Ragnarsson, Ragnarsson, Kari
Mathematics · #55P42 (Secondary) #55R35 (Primary) 20J06 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #math.AT #math.GR #msc:20J06 #msc:55P42 #msc:55R35

paper · pdf · doi:10.48550/arxiv.math/0502577

10 pages. Clarified text after Definition 1.1 and altered discussion in Section 4 following suggestions from referee. To appear in Topology

arxiv created 2005/09/12 · arxiv updated 2009/12/01

Abstract

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.

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