# Poincare duality in loop spaces

 Mathematical Conversations Topic: Poincare duality in loop spaces Speaker: Nancy Hingston Affiliation: The College of New Jersey Date: Wednesday, March 22 Time/Room: 6:00pm - 7:00pm/Dilworth Room

Geometers since Morse are interested in Morse Theory on the free loop space $LM$ of a Riemannian manifold $M$, because the critical points of the energy function on $LM$ are the closed geodesics on $M$. I will discuss an observed symmetry of the Morse theory that looks a lot like Poincaré duality. So far there are many manifestations of this symmetry principle, but no clear statement.