Riemannian foliations and geometric quantization

2022/09/28 by Yi Lin, Yiannis Loizides, Lin, Yi +5
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2209.13766

openalex publication_date 2022/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-reduction theorem in this context. Examples related to symplectic toric quasi-folds, suspensions of isometric actions of discrete groups, and K-contact manifolds are discussed.

Related

• Shifted geometric quantization
• Geometric quantization of symplectic foliations
• Quantization of Presymplectic Manifolds and Circle Actions
• Geometric quantization of b-symplectic manifolds
• Functorial quantization and the Guillemin-Sternberg conjecture