Graduate Student Colloquium
Maxim Laurentiu
UIC
An elementary introduction to intersection homology
Abstract: Manifolds -- spaces that locally look uniform, at each point and in each
direction -- have an amazing hidden symmetry, called Poincaré duality. This
reflects the existence of a non-degenerate, symmetric bilinear form on their
rational homology groups, and turns out to be a very powerful tool for the study
of manifolds.
Singular spaces, for example a pinched torus, have no such structure on their
homology groups. Surprisingly though, much of the manifold theory (including
Poincaré duality) can be recovered for a large class of singular spaces if we
consider not the usual homology, but instead intersection homology.
I will give an elementary introduction to intersection homology, following the
original approach of Goresky-MacPherson.
Friday October 7, 2005 at 3:00 PM in SEO 636