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Geometric Quantization of real polarizations via sheaves
Miranda Galcerán, Eva; Presas, Francisco
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
Mathematical physics
Geometry, Differencial
Física matemàtica
Geometria diferencial
Classificació AMS::53 Differential geometry
Attribution-NonCommercial-NoDerivs 3.0 Spain
Article - Draft

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