**Memoirs of the American Mathematical Society**

2010;
60 pp;
Softcover

MSC: Primary 53;

Print ISBN: 978-0-8218-4714-5

Product Code: MEMO/207/971

List Price: $61.00

Individual Member Price: $36.60

**Electronic ISBN: 978-1-4704-0585-4
Product Code: MEMO/207/971.E**

List Price: $61.00

Individual Member Price: $36.60

# Locally Toric Manifolds and Singular Bohr-Sommerfeld Leaves

Share this page
*Mark D. Hamilton*

When geometric quantization is applied to a manifold using a real
polarization which is “nice enough”, a result of
Śniatycki says that the quantization can be found by counting
certain objects, called Bohr-Sommerfeld leaves. Subsequently, several
authors have taken this as motivation for counting Bohr-Sommerfeld
leaves when studying the quantization of manifolds which are less
“nice”.

In this paper, the author examines the quantization of compact
symplectic manifolds that can locally be modelled by a toric manifold,
using a real polarization modelled on fibres of the moment map. The
author computes the results directly and obtains a theorem similar to
Śniatycki's, which gives the quantization in terms of counting
Bohr-Sommerfeld leaves. However, the count does not include the
Bohr-Sommerfeld leaves which are singular. Thus the quantization
obtained is different from the quantization obtained using a
Kähler polarization.

#### Table of Contents

# Table of Contents

## Locally Toric Manifolds and Singular Bohr-Sommerfeld Leaves

- Chapter 1. Introduction 18 free
- 1.1. Methods 29 free

- Chapter 2. Background 512
- Chapter 3. The cylinder 1522
- Chapter 4. The complex plane 2936
- Chapter 5. Example: S2 3542
- Chapter 6. The multidimensional case 3744
- Chapter 7. A better way to calculate cohomology 4148
- Chapter 8. Piecing and glueing 5158
- Chapter 9. Real and Kähler polarizations compared 5764
- Bibliography 5966