{"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}
引用次数: 1
Abstract
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.