Locally Toric Manifolds And Singular Bohr Sommerfeld Leaves
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Locally Toric Manifolds and Singular Bohr-Sommerfeld Leaves
Author | : Mark D. Hamilton |
Publisher | : |
Total Pages | : 60 |
Release | : 2010 |
Genre | : MATHEMATICS |
ISBN | : 9781470405854 |
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"When geometric quantization is applied to a manifold using a real polarization which is 'nice enough', a result of Sniatycki 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 Sniatycki'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."--Publisher's description.
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