Cellularization of classifying spaces and fusion properties of finite groups

R. J. Flores; J. Scherer

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Cellularization of classifying spaces and fusion properties of finite groups

R. J. Flores·J. Scherer

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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.

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R. J. Flores, J. Scherer. 2005-01-25. Cellularization of classifying spaces and fusion properties of finite groups. https://arxiv.org/abs/math/0501442

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