{"title":"Liouville polarizations and the rigidity of their Lagrangian skeleta in dimension $4$","authors":"Emmanuel Opshtein, Felix Schlenk","doi":"arxiv-2407.09408","DOIUrl":null,"url":null,"abstract":"The main theme of this paper is the introduction of a new type of\npolarizations, suited for some open symplectic manifolds, and their\napplications. These applications include symplectic embedding results that\nanswer a question by Sackel-Song-Varolgunes-Zhu and Brendel, new Lagrangian\nnon-removable intersections at small scales, and a novel phenomenon of\nLegendrian barriers in contact geometry.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-07-12","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-2407.09408","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
The main theme of this paper is the introduction of a new type of
polarizations, suited for some open symplectic manifolds, and their
applications. These applications include symplectic embedding results that
answer a question by Sackel-Song-Varolgunes-Zhu and Brendel, new Lagrangian
non-removable intersections at small scales, and a novel phenomenon of
Legendrian barriers in contact geometry.
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