{"title":"传奇结的⁰极限","authors":"Georgios Dimitroglou Rizell, Michael Sullivan","doi":"10.1090/btran/189","DOIUrl":null,"url":null,"abstract":"Take a sequence of contactomorphisms of a contact three-manifold that \n\n \n \n C\n 0\n \n C^0\n \n\n-converges to a homeomorphism. If the images of a Legendrian knot limit to a smooth knot under this sequence, we show that it is contactomorphic to the original knot. We prove this by establishing that, on one hand, non–Legendrian knots admit a type of contact-squashing (similar to squeezing) onto transverse knots while, on the other hand, Legendrian knots do not admit such a squashing. The non-trivial input from contact topology that is needed is (a local version of) the Thurston–Bennequin inequality.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":" 46","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"𝐶⁰-limits of Legendrian knots\",\"authors\":\"Georgios Dimitroglou Rizell, Michael Sullivan\",\"doi\":\"10.1090/btran/189\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Take a sequence of contactomorphisms of a contact three-manifold that \\n\\n \\n \\n C\\n 0\\n \\n C^0\\n \\n\\n-converges to a homeomorphism. If the images of a Legendrian knot limit to a smooth knot under this sequence, we show that it is contactomorphic to the original knot. We prove this by establishing that, on one hand, non–Legendrian knots admit a type of contact-squashing (similar to squeezing) onto transverse knots while, on the other hand, Legendrian knots do not admit such a squashing. The non-trivial input from contact topology that is needed is (a local version of) the Thurston–Bennequin inequality.\",\"PeriodicalId\":377306,\"journal\":{\"name\":\"Transactions of the American Mathematical Society, Series B\",\"volume\":\" 46\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the American Mathematical Society, Series B\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/btran/189\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the American Mathematical Society, Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/btran/189","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
取一个接触三芒星的接触同构序列，C 0 C^0 -converges to a homeomorphism。如果在这个序列下，一个 Legendrian 结的图像极限到一个光滑结，我们就可以证明它与原来的结是接触同构的。我们证明这一点的方法是，一方面，非勒根结允许一种类型的接触挤压（类似于挤压）到横向结上，而另一方面，勒根结不允许这种挤压。这就需要从接触拓扑学中输入（局部版本的）瑟斯顿-贝内金不等式（Thurston-Bennequin inequality）。
Take a sequence of contactomorphisms of a contact three-manifold that
C
0
C^0
-converges to a homeomorphism. If the images of a Legendrian knot limit to a smooth knot under this sequence, we show that it is contactomorphic to the original knot. We prove this by establishing that, on one hand, non–Legendrian knots admit a type of contact-squashing (similar to squeezing) onto transverse knots while, on the other hand, Legendrian knots do not admit such a squashing. The non-trivial input from contact topology that is needed is (a local version of) the Thurston–Bennequin inequality.
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