# Geometric Quantization of real polarizations via sheaves

In this article we develop tools to compute the Geometric Quantization of a symplectic manifold with respect to a regular Lagrangian foliation via sheaf cohomology. The starting point is the definition of representation spaces due to Kostant. We check that the associated sheaf cohomology apparatus satisfies Mayer-Vietoris and K\"unneth formulae. As a consequence, new proofs of classical results for fibrations are obtained. In the general case of Lagrangian foliations, we compute Geometric Quantization with respect to almost any generic regular Lagrangian foliation on a 2-torus.

Article:
Geometric Quantization of real polarizations via sheaves
Authors:
Eva Miranda, Francisco Presas
Journal:
ArXiv preprint
Year:
2013
URL:
http://arxiv.org/abs/1301.2551