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Cellular properties of nilpotent spaces
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2015 (English)In: Geometry and Topology, ISSN 1465-3060, E-ISSN 1364-0380, Vol. 19, no 5, 2741-2766 p.Article in journal (Refereed) PublishedText
Abstract [en]

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 z(k) X 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 P-n X, and that any nilpotent space for which the space of pointed self-maps map(*) (X, X) is "canonically" discrete must be aspherical.

Place, publisher, year, edition, pages
GEOMETRY & TOPOLOGY PUBLICATIONS , 2015. Vol. 19, no 5, 2741-2766 p.
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URN: urn:nbn:se:kth:diva-180179DOI: 10.2140/gt.2015.19.2741ISI: 000365637300007ScopusID: 2-s2.0-84945905928OAI: diva2:892688

QC 20150111

Available from: 2016-01-11 Created: 2016-01-07 Last updated: 2016-01-11Bibliographically approved

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Chacholski, Wojciech
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