{"title":"完全实数协和的拉格朗日近似法","authors":"Georgios Dimitroglou Rizell","doi":"arxiv-2408.16614","DOIUrl":null,"url":null,"abstract":"We show that two-dimensional totally real concordances can be approximated by\nLagrangian concordances after sufficiently many positive and negative\nstabilisations of the Legendrian boundaries. The applications of this result\nare the construction of knotted Lagrangian concordances, and knotted Lagrangian\ntori in symplectisations of overtwisted contact manifolds.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lagrangian Approximation of Totally Real Concordances\",\"authors\":\"Georgios Dimitroglou Rizell\",\"doi\":\"arxiv-2408.16614\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that two-dimensional totally real concordances can be approximated by\\nLagrangian concordances after sufficiently many positive and negative\\nstabilisations of the Legendrian boundaries. The applications of this result\\nare the construction of knotted Lagrangian concordances, and knotted Lagrangian\\ntori in symplectisations of overtwisted contact manifolds.\",\"PeriodicalId\":501155,\"journal\":{\"name\":\"arXiv - MATH - Symplectic Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-29\",\"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-2408.16614\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Symplectic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.16614","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Lagrangian Approximation of Totally Real Concordances
We show that two-dimensional totally real concordances can be approximated by
Lagrangian concordances after sufficiently many positive and negative
stabilisations of the Legendrian boundaries. The applications of this result
are the construction of knotted Lagrangian concordances, and knotted Lagrangian
tori in symplectisations of overtwisted contact manifolds.
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