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.
Notes on file formats
Colin Rourke, Brian Sanderson
Mathematics Institute, University of Warwick
Coventry CV4 7AL, UK
Email: cpr@maths.warwick.ac.uk, bjs@maths.warwick.ac.uk
GT home page
