Intersection Cohomology

This volume contains the Notes of a seminar on Intersection Ho- logy which met weekly during the Spring 1983 at the University of Bern, Switzerland. Its main purpose was to give an introduction to the pie- wise linear and sheaf theoretic aspects of the theory Goresky and R. MacPherson, Topology 19(1980) 135-162, Inv. Math. 72(1983) 17-130) and to some of its applications, for an audience assumed to have some familiarity with algebraic topology and sheaf theory. These Notes can be divided roughly into three parts. The first one to is chiefly devoted to the piecewise linear version of the theory: In A. Haefliger describes intersection homology in the piecewise linear context; II, by N. Habegger, prepares the transition to the sheaf theoretic point of view and III, by M. Goresky and R. Mac- Pherson, provides an example of computation of intersection homology. The spaces on which intersection homology is defined are assumed to admit topological stratifications with strong local triviality p- perties (cf I or V). Chapter IV, by N. A''Campo, gives some indications on how the existence of such stratifications is proved on complex analytic spaces. The primary goal of V is to describe intersection homology, or rather cohomology, in the framework of sheaf theory and to prove its main basic properties, following the second paper quoted above. Fa- liarity with standard sheaf theory, as in Godement''s book, is assumed.