  This paper defines new intersection homology groups. The basic idea is this.
Ordinary homology is locally trivial. Intersection homology is not. It may have
significant local cycles. A local-global cycle is defined to be a family of
such local cycles that is, at the same time, a global cycle. The motivating
problem is the numerical characterisation of the flag vectors of convex
polytopes. Central is a study of the cycles on a cone and a cylinder, in terms
of those on the base. This leads to the topological definition of local-global
intersection homology, and a formula for the expected Betti numbers of toric
varieties. Various related questions are also discussed.
