Stratified fibrations and the intersection homology of the regular neighborhoods of bottom strata

Abstract

In this paper, we develop Leray–Serre-type spectral sequences to compute the intersection homology of the regular neighborhood and deleted regular neighborhood of the bottom stratum of a stratified PL-pseudomanifold. The E 2 terms of the spectral sequences are given by the homology of the bottom stratum with a local coefficient system whose stalks consist of the intersection homology modules of the link of this stratum (or the cone on this link). In the course of this program, we establish the properties of stratified fibrations over unfiltered base spaces and of their mapping cylinders. We also prove a folk theorem concerning the stratum-preserving homotopy invariance of intersection homology.