Postnikov pieces and $B\mathbb {Z}/p$-homotopy theory
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- by Natàlia Castellana, Juan A. Crespo and Jérôme Scherer PDF
- Trans. Amer. Math. Soc. 359 (2007), 1099-1113 Request permission
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.References
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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
- 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 - © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 1099-1113
- MSC (2000): Primary 55R35; Secondary 55P60, 55P20, 20F18
- DOI: https://doi.org/10.1090/S0002-9947-06-03957-2
- MathSciNet review: 2262843