{"title":"Bohr-Sommerfeld profile surgeries and Disk Potentials","authors":"Soham Chanda","doi":"arxiv-2409.11603","DOIUrl":null,"url":null,"abstract":"We construct a new surgery type operation by switching between two exact\nfillings of Legendrians which we call a BSP surgery. In certain cases, this\nsurgery can preserve monotonicity of Lagrangians. We prove a wall-crossing type\nformula for the change of the disk-potential under surgery with Bohr-Sommerfeld\nprofiles. As an application, we show that Biran's circle-bundle lifts admit a\nBohr-Sommerfeld type surgery. We use the wall-crossing theorem about\ndisk-potentials to construct exotic monotone Lagrangian tori in $\\bP^n$.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":"98 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Symplectic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11603","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We construct a new surgery type operation by switching between two exact
fillings of Legendrians which we call a BSP surgery. In certain cases, this
surgery can preserve monotonicity of Lagrangians. We prove a wall-crossing type
formula for the change of the disk-potential under surgery with Bohr-Sommerfeld
profiles. As an application, we show that Biran's circle-bundle lifts admit a
Bohr-Sommerfeld type surgery. We use the wall-crossing theorem about
disk-potentials to construct exotic monotone Lagrangian tori in $\bP^n$.
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