2003/04/17 by Eli Hawkins, Hawkins, Eli
Mathematics · #19K56 #46L85 #53D50 #81S10 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #math.DG #math.KT #math.QA #msc:19K56 #msc:46L85 #msc:53D50 #msc:81S10
paper · pdf · doi:10.48550/arxiv.math/0304246
69 pages. AMS-LaTeX, AMS fonts, euler
arxiv created 2003/04/17 · openalex publication_date 2003/04/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The standard (Berezin-Toeplitz) geometric quantization of a compact Kaehler manifold is restricted by integrality conditions. These restrictions can be circumvented by passing to the universal covering space, provided that the lift of the symplectic form is exact. I relate this construction to the Baum-Connes assembly map and prove that it gives a strict quantization of the manifold. I also propose a further generalization, classify the required structure, and provide a means of computing the resulting algebras. These constructions involve twisted group C*-algebras of the fundamental group which are determined by a group cocycle constructed from the cohomology class of the symplectic form.