{"title":"Infinitely many non-conjugate braid representatives of links","authors":"Reiko Shinjo , Alexander Stoimenow","doi":"10.1016/j.jpaa.2025.107964","DOIUrl":null,"url":null,"abstract":"<div><div>We prove that under a fairly general condition (that the edge strands are not fixed by the braid permutation) an iterated exchange move gives infinitely many non-conjugate braid representatives of links. More precisely, almost all braids obtained by iterated positive exchange moves are pairwise non-conjugate. As a consequence, every link with no trivial components has infinitely many conjugacy classes of <em>n</em>-braid representatives if and only if it has one admitting an exchange move.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107964"},"PeriodicalIF":0.8000,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404925001033","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/4/10 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that under a fairly general condition (that the edge strands are not fixed by the braid permutation) an iterated exchange move gives infinitely many non-conjugate braid representatives of links. More precisely, almost all braids obtained by iterated positive exchange moves are pairwise non-conjugate. As a consequence, every link with no trivial components has infinitely many conjugacy classes of n-braid representatives if and only if it has one admitting an exchange move.
期刊介绍：
The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.
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