QUANTIZATION OF MULTIPLY CONNECTED MANIFOLDS

Open Access
Author:
Hawkins, Eli John
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
August 15, 2002
Committee Members:
  • Nigel David Higson, Committee Chair
  • Paul Frank Baum, Committee Member
  • Victor Nistor, Committee Member
  • John Collins, Committee Member
Keywords:
  • K-theory
  • Noncommutative Geometry
  • Operator Algebras
  • Quantization
Abstract:
I propose that integrality obstructions to geometric quantization can be circumvented for some compact Kaehler 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.