Intersection homology and Poincaré duality on homotopically stratified spaces

Friedman, Greg¹

¹ Department of Mathematics, Texas Christian University, Box 298900, Fort Worth, TX 76129, USA

Geometry & topology, Tome 13 (2009) no. 4, pp. 2163-2204.

Résumé

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.

Détail

DOI : 10.2140/gt.2009.13.2163

Keywords: intersection homology, Poincaré duality, homotopically stratified space

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