Greg Friedman (Texas Christian University)
Title
Intersection Homology and Poincare Duality on Homotopically Stratified
Spaces
Abstract
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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