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Cellular properties of nilpotent spaces


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Author: Chachólski, Wojciech
Farjoun, Emmanuel Dror
Flores Díaz, Ramón Jesús
Scherer, Jérôme
Department: Universidad de Sevilla. Departamento de Geometría y Topología
Date: 2015-10
Published in: Geometry and Topology, 19 (5), 2741-2766.
Document type: Article
Abstract: We show that cellular approximations of nilpotent Postnikov stages are always nilpotent Postnikov stages, in particular classifying spaces of nilpotent groups are turned into classifying spaces of nilpotent groups. We use a modified Bousfield-Kan homology completion tower zkX whose terms we prove are all X–cellular for any X. As straightforward consequences, we show that if X is K–acyclic and nilpotent for a given homology theory K, then so are all its Postnikov sections PnX , and that any nilpotent space for which the space of pointed self-maps map .X; X/ is “canonically” discrete must be aspherical.
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DOI: 10.2140/gt.2015.19.2741

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