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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Postnikov pieces and $ B\mathbb{Z}/p$-homotopy theory


Authors: Natàlia Castellana, Juan A. Crespo and Jérôme Scherer
Journal: Trans. Amer. Math. Soc. 359 (2007), 1099-1113
MSC (2000): Primary 55R35; Secondary 55P60, 55P20, 20F18
Published electronically: October 16, 2006
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Abstract: We present a constructive method to compute the cellularization with respect to $ B^{m}\mathbb{Z}/p$ for any integer $ m \geq 1$ of a large class of $ H$-spaces, namely all those which have a finite number of non-trivial $ B^{m}\mathbb{Z}/p$-homotopy groups (the pointed mapping space $ \operatorname{map}_*(B^{m}\mathbb{Z}/p, X)$ is a Postnikov piece). We prove in particular that the $ B^{m}\mathbb{Z}/p$-cellularization of an $ H$-space having a finite number of $ B^{m}\mathbb{Z}/p$-homotopy groups is a $ p$-torsion Postnikov piece. Along the way, we characterize the $ B\mathbb{Z}/p^r$-cellular classifying spaces of nilpotent groups.


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Additional Information

Natàlia Castellana
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
Email: natalia@mat.uab.es

Juan A. Crespo
Affiliation: Departament de Economia i de Història Econòmica, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
Address at time of publication: Departamento de Economía, Universidad Carlos III de Madrid, E-28903 Getafe, Spain
Email: JuanAlfonso.Crespo@uab.es, jacrespo@eco.uc3m.es

Jérôme Scherer
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
Email: jscherer@mat.uab.es

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03957-2
PII: S 0002-9947(06)03957-2
Keywords: Cellularization, $H$-spaces, Postnikov pieces, nilpotent groups
Received by editor(s): November 26, 2004
Published electronically: October 16, 2006
Additional Notes: All three authors were partially supported by MEC grant MTM2004-06686
The third author was supported by the program Ramón y Cajal, MEC, Spain
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.