Local-global intersection homology

Details Local-global intersection homology Local-global intersection homology

1997-09-10

arxiv.org/abs/alg-geom/9709011v2

Mathematics

Algebraic Geometry

LaTeX 2e. 28 pages. This paper defines new intersection homology groups, that provide important new information

Scientific paper

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.

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