Intersection homology and Poincaré duality on homotopically stratified spaces

Friedman, Greg

doi:10.2140/gt.2009.13.2163

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Intersection homology and Poincaré duality on homotopically stratified spaces

Greg Friedman

Geometry & Topology 13 (2009) 2163–2204

DOI: 10.2140/gt.2009.13.2163

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

Volume 13, issue 4 (2009)