Localization of fibrations with nilpotent fibre
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.
scientific article; zbMATH DE number 3856001