Riemannian foliations and geometric quantization

Abstract

We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantizationcommutes-with-reduction theorem in this context. Examples related to symplectic toric quasifolds, suspensions of isometric actions of discrete groups, and K-contact manifolds are discussed. YI LIN, YIANNIS LOIZIDES, REYER SJAMAAR, AND YANLI SONG 6.4. Haefliger suspensions 36 Appendix A. Transverse metrics, completeness and the Molino package 36 Appendix B. Reduction theory for transverse symplectic structures 39 B.1. Transverse Hamiltonian Lie algebra actions 40 B.2. Reduction at a value 42 B.3. Reduction at a coadjoint orbit 43 B.4. Additional properties 45 References 46