Geometry & Topology Monographs 2 (1999), Proceedings of the Kirbyfest, paper no. 22, pages 455-472.

Homology stratifications and intersection homology

Colin Rourke, Brian Sanderson

Abstract. 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.

Keywords. Permutation homology, intersection homology, homology stratification, homology general position

AMS subject classification. Primary: 55N33, 57Q25, 57Q65. Secondary: 18G35, 18G60, 54E20, 55N10, 57N80, 57P05.

E-print: arXiv:math.GT/9911259

Submitted: 16 November 1998. (Revised: 8 July 1999.) Published: 21 November 1999.

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Colin Rourke, Brian Sanderson
Mathematics Institute, University of Warwick
Coventry CV4 7AL, UK

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