Riemannian foliations and geometric quantization

TL;DR

This paper develops a geometric quantization framework for presymplectic structures with Riemannian null foliations, establishing a quantization-commutes-with-reduction theorem and exploring various geometric examples.

Contribution

It introduces a novel geometric quantization approach for presymplectic structures with Riemannian null foliations and proves a key theorem relating quantization and reduction.

Findings

Quantization-commutes-with-reduction theorem proven in this context

Application to symplectic toric quasi-folds and K-contact manifolds

Examples illustrating the theory with discrete group actions

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.