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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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