接触$(+1)$-有理同调$3$-球面上的手术

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Symplectic Geometry Pub Date : 2023-04-24 DOI:10.4310/jsg.2022.v20.n5.a2

Fan Ding, Youlin Li, Zhongtao Wu

{"title":"接触$(+1)$-有理同调$3$-球面上的手术","authors":"Fan Ding, Youlin Li, Zhongtao Wu","doi":"10.4310/jsg.2022.v20.n5.a2","DOIUrl":null,"url":null,"abstract":"In this paper, sufficient conditions for contact $(+1)$-surgeries along Legendrian knots in contact rational homology $3$-spheres to have vanishing contact invariants or to be overtwisted are given. They can be applied to study contact $(\\pm 1)$-surgeries along Legendrian links in the standard contact $3$-sphere. We also obtain a sufficient condition for contact $(+1)$-surgeries along Legendrian twocomponent links in the standard contact $3$-sphere to be overtwisted via their front projections.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"18 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Contact $(+1)$-surgeries on rational homology $3$-spheres\",\"authors\":\"Fan Ding, Youlin Li, Zhongtao Wu\",\"doi\":\"10.4310/jsg.2022.v20.n5.a2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, sufficient conditions for contact $(+1)$-surgeries along Legendrian knots in contact rational homology $3$-spheres to have vanishing contact invariants or to be overtwisted are given. They can be applied to study contact $(\\\\pm 1)$-surgeries along Legendrian links in the standard contact $3$-sphere. We also obtain a sufficient condition for contact $(+1)$-surgeries along Legendrian twocomponent links in the standard contact $3$-sphere to be overtwisted via their front projections.\",\"PeriodicalId\":50029,\"journal\":{\"name\":\"Journal of Symplectic Geometry\",\"volume\":\"18 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-04-24\",\"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.2022.v20.n5.a2\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Symplectic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/jsg.2022.v20.n5.a2","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

摘要

本文给出了在接触有理同调球面上沿Legendrian结的接触$(+1)$-整形具有消失的接触不变量或超扭的充分条件。它们可以应用于研究接触$(\pm 1)$-在标准接触$3$-球面上沿Legendrian连杆的手术。我们还得到了在标准接触球面上沿Legendrian双分量连杆的接触$(+1)$-手术通过其前投影被扭转的充分条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Contact $(+1)$-surgeries on rational homology $3$-spheres

In this paper, sufficient conditions for contact $(+1)$-surgeries along Legendrian knots in contact rational homology $3$-spheres to have vanishing contact invariants or to be overtwisted are given. They can be applied to study contact $(\pm 1)$-surgeries along Legendrian links in the standard contact $3$-sphere. We also obtain a sufficient condition for contact $(+1)$-surgeries along Legendrian twocomponent links in the standard contact $3$-sphere to be overtwisted via their front projections.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Symplectic Geometry 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： 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.