Pure PGR Seminar - Poincaré Duality, Holly Paveling (Southampton) Seminar

Event details

The Poincaré Duality theorem was first stated (unproved) in 1893, and says that the kth and (n – k)th Betti numbers of a closed orientable n-manifold are equal. The modern formulation, in terms of homology and cohomology, was proved independently by Čech and Hassler Whitney in the 30's. I'll be talking about the cap product on chain groups, and the duality isomorphisms between homology and cohomology groups of manifolds. There are also some interesting generalisations to non-oriented manifolds and manifolds with boundary.