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arXiv · alg-geom/9709011

Local-global intersection homology

Jonathan Fine
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Abstract

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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Jonathan Fine. 1997-09-11. Local-global intersection homology. https://arxiv.org/abs/alg-geom/9709011

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