Cellular properties of nilpotent spaces
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
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.
IdentifiersURN: urn:nbn:se:kth:diva-180179DOI: 10.2140/gt.2015.19.2741ISI: 000365637300007ScopusID: 2-s2.0-84945905928OAI: oai:DiVA.org:kth-180179DiVA: diva2:892688
QC 201501112016-01-112016-01-072016-01-11Bibliographically approved