Lefschetz fixed point theorem for intersection homology

Abstract

We show that both the graph of f and the diagonal carry fundamental classes in the intersection homology of X x X, and that the Lefschetz number IL(f) is the intersection number of these two classes. This is exactly the procedure originally used by Lefschetz to study fixed points in manifolds using ordinary homology ILl. So the results of this paper can be viewed as an addition to the series of theorems which show that the intersection homology of a singular space behaves like the ordinary homology of a smooth variety (see [CGM], [GM 4]). Let X be an n dimensional Witt space. (See w for the definition of a Witt space. Any complex analytic variety of pure dimension k is a 2k dimensional Witt space.) A self map f of X is called placid if X can be stratified so that the dimension of the inverse image of each stratum is at most the dimension of that stratum. For example, all maps of manifolds are placid and all fiat maps of algebraic varieties are placid. The induced map