Noncommutative Differential Geometry and Twisting of Quantum Groups

Abstract

We outline the recent classification of differential structures for all main classes of quantum groups. We also outline the algebraic notion of `quantum manifold' and `quantum Riemannian manifold' based on quantum group principal bundles, a formulation that works over general unital algebras.

10 pages, to appear Proc. LMS Symposium Quantum Groups, Durham, 1999. This intro for mathematicians