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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Intersection homology and Poincaré duality on homotopically stratified spaces

Greg Friedman

Geometry & Topology 13 (2009) 2163–2204
Abstract

We show that intersection homology extends Poincaré duality to manifold homotopically stratified spaces (satisfying mild restrictions). These spaces were introduced by Quinn to provide “a setting for the study of purely topological stratified phenomena, particularly group actions on manifolds.” The main proof techniques involve blending the global algebraic machinery of sheaf theory with local homotopy computations. In particular, this includes showing that, on such spaces, the sheaf complex of singular intersection chains is quasi-isomorphic to the Deligne sheaf complex.

Keywords
intersection homology, Poincaré duality, homotopically stratified space
Mathematical Subject Classification 2000
Primary: 55N33, 57N80, 57P99
References
Publication
Received: 18 April 2007
Revised: 16 April 2009
Accepted: 24 April 2009
Published: 16 May 2009
Proposed: Steve Ferry
Seconded: Ralph Cohen, Tom Goodwillie
Authors
Greg Friedman
Department of Mathematics
Texas Christian University
Box 298900
Fort Worth, TX 76129
USA