Leray-Serre Spectral Sequence for Quasi-Fibrations

Abstract

Let f : X âŸ¶ Y be a map between two spaces for which Y is stratified such that f is a fibration over each open stratum. We find some spectral sequences to compote the homology of X in terms of the homology of Y and that of the fibers. We apply this to give a Lefschetz theorem for the degeneracy loci of a morphism between holomorphic bundles on a complex manifold.