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Postnikov pieces and -homotopy theory

Authors:	Natà lia Castellana Juan A Crespo Jé rô me Scherer

Institution:	Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain ; Departament de Economia i de Història Econòmica, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain ; Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain

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 -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 -space having a finite number of $B^{m}\mathbb{Z}/p$ -homotopy groups is a -torsion Postnikov piece. Along the way, we characterize the $B\mathbb{Z}/p^r$ -cellular classifying spaces of nilpotent groups.

Keywords:	Cellularization $H$-spaces Postnikov pieces nilpotent groups

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