Homology stratifications and intersection homology

Details Homology stratifications and intersection homology Homology stratifications and intersection homology

1999-11-21

arxiv.org/abs/math/9911259v1

Geom. Topol. Monogr. 2 (1999), 455-472

Mathematics

Geometric Topology

18 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper22.abs.html

Scientific paper

A homology stratification is a filtered space with local homology groups constant on strata. Despite being used by Goresky and MacPherson [Intersection homology theory: II, Inventiones Mathematicae, 71 (1983) 77-129] in their proof of topological invariance of intersection homology, homology stratifications do not appear to have been studied in any detail and their properties remain obscure. Here we use them to present a simplified version of the Goresky-MacPherson proof valid for PL spaces, and we ask a number of questions. The proof uses a new technique, homology general position, which sheds light on the (open) problem of defining generalised intersection homology.

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