Quantization of multiply connected manifolds

by 1973- Hawkins, Eli

I propose that integrality obstructions to geometric quantization can be circumvented for some compact Kähler manifolds by passing to the universal covering space. This can be done if the lift of the symplectic form to the universal covering space is cohomologically trivial. I prove that this construction does give a strict quantization. The construction is related to the Baum-Connes assembly map. I also propose a type of further generalized Toeplitz construction, classify the structure involved, and give a simple construction for the resulting algebras. These constructions involve twisted group C?-algebras of the fundamental group. These are determined by a group cocycle constructed from the cohomology class of the symplectic form.