Localization of fibrations with nilpotent fibre
type: Item
instance of: scholarly article
title: Localization of fibrations with nilpotent fibre
zbMATH Open document ID: 0538.55006
DOI: 10.1007/BF01159184
author: Irene Llerena Rodríguez
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173547
review text: Recently, \textit{P. Hilton} [Nilpotente Gruppen und nilpotente Räume, Lect. Notes Math. 1053 (1984)] has developed a localization theory for nilpotent crossed-modules which relativizes that for nilpotent groups. In an earlier paper [Collect. Math. 33, 177-185 (1982; Zbl 0526.55012)] we have relativized the topological case of nilpotent spaces and defined a localization for nilpotent fibre maps f: \(E\to B\) (i.e. such that \(\pi_ 1E\) acts nilpotently on the homotopy groups of the fibre). In this note we consider the more general situation of fibrations with nilpotent fibre and develop a localization theory for such fibrations. We argue stepwise on the Moore-Postnikov factorization of f. The essential point in our generalization is that now the Moore-Postnikov system of f does not admit a principal refinement and we need to use the existence of a universal fibration classifying the K(G,1)-fibrations.
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 55S45
Mathematics Subject Classification ID: 55R05
zbMATH DE Number: 3856001
zbMATH Keywords: fibrations with nilpotent fibre
zbMATH Keywords: localization
zbMATH Keywords: Moore-Postnikov factorization
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3856001