{"title":"谢卢金-契卡诺夫-霍费尔公设消失的传奇人","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":"{\"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}","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}
Legendrians with vanishing Shelukhin–Chekanov–Hofer metric
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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