{"title":"On linking of Lagrangian tori in $\\mathbb{R}^4$","authors":"Laurent Cot'e","doi":"10.4310/jsg.2020.v18.n2.a3","DOIUrl":null,"url":null,"abstract":"We prove some results about linking of Lagrangian tori in the symplectic vector space $(\\mathbb{R}^4, \\omega)$. We show that certain enumerative counts of holomophic disks give useful information about linking. This enables us to prove, for example, that any two Clifford tori are unlinked in a strong sense. We extend work of Dimitroglou Rizell and Evans on linking of monotone Lagrangian tori to a class of non-monotone tori in $\\mathbb{R}^4$ and also strengthen their conclusions in the monotone case in $\\mathbb{R}^4$.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-20","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/jsg.2020.v18.n2.a3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We prove some results about linking of Lagrangian tori in the symplectic vector space $(\mathbb{R}^4, \omega)$. We show that certain enumerative counts of holomophic disks give useful information about linking. This enables us to prove, for example, that any two Clifford tori are unlinked in a strong sense. We extend work of Dimitroglou Rizell and Evans on linking of monotone Lagrangian tori to a class of non-monotone tori in $\mathbb{R}^4$ and also strengthen their conclusions in the monotone case in $\mathbb{R}^4$.