{"title":"Legendrians with vanishing Shelukhin–Chekanov–Hofer metric","authors":"Lukas Nakamura","doi":"10.4310/arkiv.2024.v62.n1.a8","DOIUrl":null,"url":null,"abstract":"We show that the Legendrian lift of an exact, displaceable Lagrangian has vanishing Shelukhin–Chekanov–Hofer pseudo-metric by lifting an argument due to Sikorav to the contactization. In particular, this proves the existence of such Legendrians, providing counterexamples to a conjecture of Rosen and Zhang.","PeriodicalId":501438,"journal":{"name":"Arkiv för Matematik","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arkiv för Matematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/arkiv.2024.v62.n1.a8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We show that the Legendrian lift of an exact, displaceable Lagrangian has vanishing Shelukhin–Chekanov–Hofer pseudo-metric by lifting an argument due to Sikorav to the contactization. In particular, this proves the existence of such Legendrians, providing counterexamples to a conjecture of Rosen and Zhang.
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