Memoirs of the American Mathematical Society 2010; 60 pp; softcover Volume: 207 ISBN10: 0821847147 ISBN13: 9780821847145 List Price: US$61 Individual Members: US$36.60 Institutional Members: US$48.80 Order Code: MEMO/207/971
 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 BohrSommerfeld leaves. Subsequently, several authors have taken this as motivation for counting BohrSommerfeld 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 BohrSommerfeld leaves. However, the count does not include the BohrSommerfeld leaves which are singular. Thus the quantization obtained is different from the quantization obtained using a Kähler polarization. Table of Contents  Introduction
 Background
 The cylinder
 The complex plane
 Example: \(S^2\)
 The multidimensional case
 A better way to calculate cohomology
 Piecing and glueing
 Real and Kähler polarizations compared
 Bibliography
