Greg Friedman (Texas Christian University)


Intersection Homology and Poincare Duality on Homotopically Stratified Spaces


Intersection homology was developed as a tool for extending Poincare duality to pseudomanifolds, such as algebraic varieties, which are not manifolds but are made up of manifolds of various dimensions (the strata) that are glued together in a manner prescribed by certain rigid local topological conditions. By contrast, manifold homotopically stratified spaces also comprise manifold strata, but the attachment of strata is described by homotopy theoretic conditions. These spaces arise naturally, for example, as quotient spaces of certain topological group actions on manifolds. We will review the basics of intersection homology theory and show that it extends Poincare duality to these homotopically stratified spaces.

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