{"title":"b -辛环流形的Bohr-Sommerfeld量化","authors":"Pau Mir, Eva Miranda, Jonathan Weitsman","doi":"10.4310/pamq.2023.v19.n4.a15","DOIUrl":null,"url":null,"abstract":"We introduce a Bohr–Sommerfeld quantization for bsymplectic toric manifolds and show that it coincides with the formal geometric quantization of $\\href{ https://mathscinet.ams.org/mathscinet/relay-station?mr=3804693}{[\\textrm{GMW18b}]}$. In particular, we prove that its dimension is given by a signed count of the integral points in the moment polytope of the torus action on the manifold.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Bohr–Sommerfeld quantization of $b$-symplectic toric manifolds\",\"authors\":\"Pau Mir, Eva Miranda, Jonathan Weitsman\",\"doi\":\"10.4310/pamq.2023.v19.n4.a15\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a Bohr–Sommerfeld quantization for bsymplectic toric manifolds and show that it coincides with the formal geometric quantization of $\\\\href{ https://mathscinet.ams.org/mathscinet/relay-station?mr=3804693}{[\\\\textrm{GMW18b}]}$. In particular, we prove that its dimension is given by a signed count of the integral points in the moment polytope of the torus action on the manifold.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-11-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/pamq.2023.v19.n4.a15\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/pamq.2023.v19.n4.a15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Bohr–Sommerfeld quantization of $b$-symplectic toric manifolds
We introduce a Bohr–Sommerfeld quantization for bsymplectic toric manifolds and show that it coincides with the formal geometric quantization of $\href{ https://mathscinet.ams.org/mathscinet/relay-station?mr=3804693}{[\textrm{GMW18b}]}$. In particular, we prove that its dimension is given by a signed count of the integral points in the moment polytope of the torus action on the manifold.
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