1997/09/10 by Jonathan Fine, Fine, Jonathan
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.alg-geom/9709011
openalex publication_date 1997/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.