| Titre : | Locally toric manifolds and singular Bohr-Sommerfeld leaves | | Type de document : | texte imprimé | | Auteurs : | Mark D. HAMILTON, Auteur | | Editeur : | Providence, R. I. [Etats Unis] : American Mathematical Society | | Année de publication : | cop. 2010 | | Collection : | Memoirs of the American Mathematical Society, ISSN 0065-9266 num. 971 | | Importance : | V-60 p. | | ISBN/ISSN/EAN : | 978-0-8218-4714-5 | | Langues : | Anglais | | Catégories : | 53D50
| | Mots-clés : | quantification géométrique | | Résumé : | When geometric quantization is applied to a manifold using a real polarization which is ``nice enough'', a result of ?niatycki 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, we examine 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. We compute the results directly, and obtain a theorem similar to ?niatycki'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.
| | Note de contenu : | bibliogr. |
Locally toric manifolds and singular Bohr-Sommerfeld leaves [texte imprimé] / Mark D. HAMILTON, Auteur . - Providence, R. I. (Etats Unis) : American Mathematical Society, cop. 2010 . - V-60 p.. - ( Memoirs of the American Mathematical Society, ISSN 0065-9266; 971) . ISBN : 978-0-8218-4714-5 Langues : Anglais | Catégories : | 53D50
| | Mots-clés : | quantification géométrique | | Résumé : | When geometric quantization is applied to a manifold using a real polarization which is ``nice enough'', a result of ?niatycki 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, we examine 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. We compute the results directly, and obtain a theorem similar to ?niatycki'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.
| | Note de contenu : | bibliogr. |
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Locally toric manifolds and singular Bohr-Sommerfeld leaves (cop. 2010)
