On the equivalence of some spectral sequences for Serre fibrations

Several different constructions of a spectral sequence for a Serre fibration over a compact simply connected manifold are considered in this paper. Namely, we consider the spectral sequence for the minimal model of the fibration, along with the spectral sequences arising from the Cech filtration in the complexes and , where is a covering of the base . It is known that all these spectral sequences have the same terms and converge to the cohomology of the total space . A new natural isomorphism of these spectral sequences is constructed in every term with . It is also proved that in the case of a smooth locally trivial fibration these spectral sequences are isomorphic to the spectral sequences of the complex of smooth forms and of the Cech-de Rham complex. It is therefore established that all these constructions give the same spectral sequence, starting from the term. Bibliography: 9 titles.