{"title":"松散Legendrian嵌入的正回路及其应用","authors":"Guogang Liu","doi":"10.4310/JSG.2020.V18.N3.A9","DOIUrl":null,"url":null,"abstract":"In this paper, we prove that there exist contractible positive loops of Legendrian embeddings based at any loose Legendrian submanifold. As an application, we define a partial order on Cont0(M, ξ), called strong orderability, and prove that overtwisted contact manifolds are not strongly orderable.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"23 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Positive loops of loose Legendrian embeddings and applications\",\"authors\":\"Guogang Liu\",\"doi\":\"10.4310/JSG.2020.V18.N3.A9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we prove that there exist contractible positive loops of Legendrian embeddings based at any loose Legendrian submanifold. As an application, we define a partial order on Cont0(M, ξ), called strong orderability, and prove that overtwisted contact manifolds are not strongly orderable.\",\"PeriodicalId\":50029,\"journal\":{\"name\":\"Journal of Symplectic Geometry\",\"volume\":\"23 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Symplectic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/JSG.2020.V18.N3.A9\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Symplectic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/JSG.2020.V18.N3.A9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Positive loops of loose Legendrian embeddings and applications
In this paper, we prove that there exist contractible positive loops of Legendrian embeddings based at any loose Legendrian submanifold. As an application, we define a partial order on Cont0(M, ξ), called strong orderability, and prove that overtwisted contact manifolds are not strongly orderable.
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Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.
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