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Journal of the London Mathematical Society Advance Access originally published online on August 2, 2007
Journal of the London Mathematical Society 2007 76(1):41-56; doi:10.1112/jlms/jdm031
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© 2007 London Mathematical Society

Cellularization of classifying spaces and fusion properties of finite groups

Ramón J. Flores

Departamento de Estadística
Universidad Carlos III de Madrid
C/Madrid 126
E-28903 Getafe
Spain
rflores{at}est-econ.uc3m.es

Jérôme Scherer

Departament de Matemàtiques
Universitat Autónoma de Barcelona
E-08193 Bellaterra
Spain

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 and compute explicitly the cellularization.

jscherer{at}mat.uab.es

2000 Mathematics Subject Classification 55P60, 20D20 (primary), 55R37, 55Q05 (secondary).

Both authors are supported by MEC grant MTM2004-06686 and the second author by the Ramón y Cajal program, MEC, Spain.

Received July 4, 2005; revised September 27, 2006; published online August 2, 2007.


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