# What is ... intersection homology?. University of Michigan, Ann Arbor. February 17, 2009

Lecture

Invited Lectures ; The homology of a compact closed n-manifold X satisfies Poincare duality: the intersection pairing between degree i and degree n-i homology is a perfect pairing over a field. When X has singularities, Poincare duality may fail to hold. Nonetheless, in the 1980's Goresky and MacPherson defined a topological invariant, the intersection homology, of a space X which satisfies Poincare duality even if X is singular; for a smooth space X, intersection homology agrees with ordinary homology. Intersection homology crops up in many places, from analysis to representation theory. In this talk I will give an informal introduction to intersection homology and some of its applications.

### Service Performed By

- Saper, Leslie Professor of Mathematics

### Date

- February 17, 2009

### Host Organization

- University of Michigan, Ann Arbor