Cellularization of classifying spaces and fusion properties of finite groups

Details Cellularization of classifying spaces and fusion properties of finite groups Cellularization of classifying spaces and fusion properties of finite groups

2005-01-25

arxiv.org/abs/math/0501442v1

Mathematics

Algebraic Topology

18 pages

Scientific paper

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.

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