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Locally toric manifolds and singular Bohr-Sommerfeld leaves / Mark D. HAMILTON (cop. 2010)
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. Exemplaires
Code-barres Cote Support Localisation Section Disponibilité 21419 854/971 Livre Recherche Salle Disponible