The fibre-cofibre construction and its applications
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.
homotopy spectral sequence of a cofibration
scientific article; zbMATH DE number 4058430
scientific article