Postnikov pieces and 𝐵ℤ/𝕡-homotopy theory

Castellana, Natàlia; Crespo, Juan; Scherer, Jérôme

doi:10.1090/S0002-9947-06-03957-2

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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