QUANTUM HALL-EFFECT ON THE HYPERBOLIC PLANE

In this paper, we study both the continuous model and the discrete mod el of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an i mprimitivity algebra of observables. We define a twisted analogue of t he Kasparov map, which enables us to use the pairing between K-theory and cyclic cohomology theory, to identify this geometric invariant wit h a topological index, thereby proving the integrality of the Hall con ductivity in this case.