Stratified simplices and intersection homology

Intersection homology is obtained from ordinary homology by imposing conditions on how the embedded simplices meet the strata of a space X . In this way, for the middle perversity, properties such as strong Lefschetz are preserved. This paper defines local-global intersection homology groups, that record global information about the singularities of X . They differ from intersection homology in that stratified rather than ordinary simplices are used. An example of such is σj × Cσi, where σi and σj are ordinary simplices, and C is the coning operator. The paper concludes with a sketch of the relationship between local-global homology and the geometry of convex polytopes. This paper is a more formal exposition of part of the author’s Local-global intersection homology, alg-geom/9709011.