Maxim Laurentiu : An elementary introduction to intersection homology

Posted by Alexander Furman , part of the Graduate Student Colloquium.

At

Oct. 7, 2005, 3 p.m.

In

SEO 636

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.