Kolloquium des Graduiertenkollegs Gruppen und Geometrie

Donnerstag, 24.05.2007


Dr. Hyun Jeong Kim

"KK-theoretic Poincaré duality"


Abstract:

Classical Poincaré duality says that for an oriented compact n-dimensional manifold, there is a canonical isomorphism between the p-homology group and the (n-p)-cohomology group of the manifold. KK-duality was formulated by Connes, Kasparov and Skandalis as a noncommutative analogue of the classical duality, which gives a canonical isomorphism between the noncommutative homology and cohomology theories, K-homology group and K-theory group for certain noncommutative algebras. In this talk, I will start with the classical case and show by some examples how a noncommutative version can be set up naturally and then I will finish by talking briefly about the main result related to Poincaré duality of twisted K-theory.