{"title":"Stable maps and hyperbolic links","authors":"Furutani,Ryoga, Koda,Yuya","doi":"10.4310/cag.2023.v31.n6.a3","DOIUrl":null,"url":null,"abstract":"A stable map of a closed orientable 3-manifold into the real plane is called a stable map of a link in the manifold if the link is contained in the set of definite fold points. We give a complete characterization of the hyperbolic links in the $3$-sphere that admit stable maps into the real plane with exactly one (connected component of a) fiber having two singular points.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"5 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cag.2023.v31.n6.a3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
A stable map of a closed orientable 3-manifold into the real plane is called a stable map of a link in the manifold if the link is contained in the set of definite fold points. We give a complete characterization of the hyperbolic links in the $3$-sphere that admit stable maps into the real plane with exactly one (connected component of a) fiber having two singular points.
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