D-branes, KK-theory and duality on noncommutative spaces

We present a new categorical classification framework for D-brane charges on noncommutative manifolds using methods of bivariant K-theory. We describe several applications including an explicit formula for D-brane charge in cyclic homology, a realignement of open string T-duality, and a general criterion for cancellation of global worldsheet anomalies.J. Brodzki, V. Mathai, J. Rosenberg and R.J. Szab