Localglobal intersection homology
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 localglobal 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 localglobal intersection homology, and a formula for the expected Betti numbers of toric varieties. Various related questions are also discussed.
 Publication:

arXiv eprints
 Pub Date:
 September 1997
 DOI:
 10.48550/arXiv.alggeom/9709011
 arXiv:
 arXiv:alggeom/9709011
 Bibcode:
 1997alg.geom..9011F
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 LaTeX 2e. 28 pages. This paper defines new intersection homology groups, that provide important new information