Kolloquium des Graduiertenkollegs Gruppen
Dr. Hyun Jeong Kim
"KK-theoretic Poincaré duality"
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.