3流形的光滑有限阶bilipschitz同胚

IF 0.8 2区数学 Q2 MATHEMATICS Journal of Topology Pub Date : 2023-09-02 DOI:10.1112/topo.12309

Lucien Grillet

{"title":"3流形的光滑有限阶bilipschitz同胚","authors":"Lucien Grillet","doi":"10.1112/topo.12309","DOIUrl":null,"url":null,"abstract":"<p>We show that, for <math>\n <semantics>\n <mrow>\n <mi>ε</mi>\n <mo>=</mo>\n <mfrac>\n <mn>1</mn>\n <mn>4000</mn>\n </mfrac>\n </mrow>\n <annotation>$\\varepsilon =\\frac{1}{4000}$</annotation>\n </semantics></math>, any action of a finite cyclic group by <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mn>1</mn>\n <mo>+</mo>\n <mi>ε</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$(1+\\varepsilon )$</annotation>\n </semantics></math>-bilipschitz homeomorphisms on a closed 3-manifold is conjugated to a smooth action.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 3","pages":"1093-1112"},"PeriodicalIF":0.8000,"publicationDate":"2023-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Smoothing finite-order bilipschitz homeomorphisms of 3-manifolds\",\"authors\":\"Lucien Grillet\",\"doi\":\"10.1112/topo.12309\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We show that, for <math>\\n <semantics>\\n <mrow>\\n <mi>ε</mi>\\n <mo>=</mo>\\n <mfrac>\\n <mn>1</mn>\\n <mn>4000</mn>\\n </mfrac>\\n </mrow>\\n <annotation>$\\\\varepsilon =\\\\frac{1}{4000}$</annotation>\\n </semantics></math>, any action of a finite cyclic group by <math>\\n <semantics>\\n <mrow>\\n <mo>(</mo>\\n <mn>1</mn>\\n <mo>+</mo>\\n <mi>ε</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$(1+\\\\varepsilon )$</annotation>\\n </semantics></math>-bilipschitz homeomorphisms on a closed 3-manifold is conjugated to a smooth action.</p>\",\"PeriodicalId\":56114,\"journal\":{\"name\":\"Journal of Topology\",\"volume\":\"16 3\",\"pages\":\"1093-1112\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-09-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Topology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12309\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12309","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

我们证明了对于ε=14000 $\varepsilon =\frac{1}{4000}$，由(1+ε) $(1+\varepsilon )$‐bilipschitz同胚构成的有限循环群在闭3‐流形上的任何作用都共轭为光滑作用。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Smoothing finite-order bilipschitz homeomorphisms of 3-manifolds

We show that, for $ε = \frac{1}{4000}$ , any action of a finite cyclic group by $(1 + ε)$ -bilipschitz homeomorphisms on a closed 3-manifold is conjugated to a smooth action.

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 Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.