{"title":"拓扑同位素和科克伦派生不变量","authors":"S. A. Melikhov","doi":"10.1090/conm/772/15493","DOIUrl":null,"url":null,"abstract":"<p>We construct a link in the <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\n <mml:semantics>\n <mml:mn>3</mml:mn>\n <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-space that is not isotopic to any PL link (non-ambiently). In fact, we show that there exist uncountably many <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I\">\n <mml:semantics>\n <mml:mi>I</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">I</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-equivalence classes of links.</p>\n\n<p>The paper also includes some observations on Cochran’s invariants <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"beta Subscript i\">\n <mml:semantics>\n <mml:msub>\n <mml:mi>β<!-- β --></mml:mi>\n <mml:mi>i</mml:mi>\n </mml:msub>\n <mml:annotation encoding=\"application/x-tex\">\\beta _i</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>.</p>","PeriodicalId":296603,"journal":{"name":"Topology, Geometry, and Dynamics","volume":"90 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Topological isotopy and Cochran’s derived invariants\",\"authors\":\"S. A. Melikhov\",\"doi\":\"10.1090/conm/772/15493\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We construct a link in the <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"3\\\">\\n <mml:semantics>\\n <mml:mn>3</mml:mn>\\n <mml:annotation encoding=\\\"application/x-tex\\\">3</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>-space that is not isotopic to any PL link (non-ambiently). In fact, we show that there exist uncountably many <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper I\\\">\\n <mml:semantics>\\n <mml:mi>I</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">I</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>-equivalence classes of links.</p>\\n\\n<p>The paper also includes some observations on Cochran’s invariants <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"beta Subscript i\\\">\\n <mml:semantics>\\n <mml:msub>\\n <mml:mi>β<!-- β --></mml:mi>\\n <mml:mi>i</mml:mi>\\n </mml:msub>\\n <mml:annotation encoding=\\\"application/x-tex\\\">\\\\beta _i</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>.</p>\",\"PeriodicalId\":296603,\"journal\":{\"name\":\"Topology, Geometry, and Dynamics\",\"volume\":\"90 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology, Geometry, and Dynamics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/conm/772/15493\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology, Geometry, and Dynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/conm/772/15493","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
我们在33 -空间中构造了一个不与任何PL链路(非环境)同位素的链路。事实上,我们证明了存在不可数的I - I -等价类。本文还包括对Cochran不变量β i \ β _i的一些观察。
Topological isotopy and Cochran’s derived invariants
We construct a link in the 33-space that is not isotopic to any PL link (non-ambiently). In fact, we show that there exist uncountably many II-equivalence classes of links.
The paper also includes some observations on Cochran’s invariants βi\beta _i.