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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 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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