New Perspectives on Poincare Duality for Singular Spaces.
Markus Banagl (Universitat Heidelberg, Germany)

Intersection homology provides a generalized form of
Poincare duality for singular spaces. After reviewing this,
we shall contrast intersection homology with a
new homology associated to singular spaces, which also
enjoys Poincare duality but is not isomorphic to
intersection homology. The new theory is expected to be
definable on a smaller class of singular spaces than
intersection homology, but when it is defined, it has a richer
algebraic structure, for instance a perversity-internal cup
product. We will discuss the new theory, at least for isolated
singularities, from several different angles, such as a
homotopy theoretic one, which constructs the theory as the
ordinary homology of certain cell complexes, and a more
analytic one, constructing it via a certain complex of
smooth differential forms. The relevance of the new theory
vis-a-vis type II string theory will also be briefly indicated.