{"title":"Contactomorphisms of the sphere without translated points","authors":"Dylan Cant","doi":"10.4310/jsg.2024.v22.n1.a1","DOIUrl":null,"url":null,"abstract":"We construct a contactomorphism of $(S^{2n-1}, \\alpha_{\\mathrm{std}})$ which does not have any translated points, providing a negative answer to a conjecture posed in $\\href{https://doi.org/10.1007/s10711-012-9741-1}{\\textrm{[San13]}}$.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Symplectic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/jsg.2024.v22.n1.a1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We construct a contactomorphism of $(S^{2n-1}, \alpha_{\mathrm{std}})$ which does not have any translated points, providing a negative answer to a conjecture posed in $\href{https://doi.org/10.1007/s10711-012-9741-1}{\textrm{[San13]}}$.
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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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