The fibre-cofibre construction and its applications
type: Item
instance of: scholarly article
title: The fibre-cofibre construction and its applications
zbMATH Open document ID: 0648.55012
DOI: 10.1016/0022-4049(88)90012-6
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: Generalizing work by \textit{Ganea} [Comment. Math. Helvet. 39, 295-322 (1965; Zbl 0142.407)] the authors consider the following situation: a fibration \(F\to^{i}E\to^{p}B\) and a map \(W\to^{f}E\) such that pf is null homotopic; then p naturally extends, giving rise to a fibration \(F'\to^{i'}E'\to^{p'}B\), where \(E'\cong Cf\) (the cone of f). The main result describes the relationship between \(H_*F\) and \(H_*F'\) as \(H_*\Omega B\)-modules and gives sufficient conditions which guarantee that \(F'\) is rationally a wedge of spheres. The applications concern the determination of the cone length of a space and the collapsing of the rational homotopy spectral sequence of a cofibration, in some particular cases.
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 55R05
Mathematics Subject Classification ID: 55P05
zbMATH DE Number: 4058430
zbMATH Keywords: fibre-cofibre construction
zbMATH Keywords: holonomy operation
zbMATH Keywords: free Lie algebra
zbMATH Keywords: rationally a wedge of spheres
zbMATH Keywords: cone length of a space
zbMATH Keywords: homotopy spectral sequence of a cofibration
author: Yves Félix
author: Jean-Claude Thomas
reviewed by: Ştefan Papadima
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90012-6
OpenAlex ID: W2053001698
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description: scientific article; zbMATH DE number 4058430