Cellularization of classifying spaces and fusion properties of finite groups

2005/01/25 by Ramón Flores, R. J. Flores, Flores, R. J. +3
Mathematics · #20D20 (Primary) 55R37 #55P60 #55Q05 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GR #msc:20D20 #msc:55P60 #msc:55Q05 #msc:55R37

paper · pdf · doi:10.48550/arxiv.math/0501442

18 pages

arxiv created 2005/01/25 · openalex publication_date 2005/01/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

One way to understand the mod p homotopy theory of classifying spaces of finite groups is to compute their BZ/p-cellularization. In the easiest cases this is a classifying space of a finite group (always a finite p-group). If not, we show that it has infinitely many non-trivial homotopy groups. Moreover they are either p-torsion free or else infinitely many of them contain p-torsion. By means of techniques related to fusion systems we exhibit concrete examples where p-torsion appears.

Related

• The cellular structure of the classifying spaces of finite groups
• Cellular approximations of fusion systems
• Postnikov pieces and BZ/p-homotopy theory
• Alternative stable homotopy classification of p-completed classifying spaces
• Assigning a classifying space to a fusion system up to F-isomorphism