{"title":"On the cosmetic crossing conjecture for special alternating links","authors":"Joseph Boninger","doi":"10.1090/bproc/184","DOIUrl":null,"url":null,"abstract":"We prove that a family of links, which includes all special alternating knots, does not admit non-nugatory crossing changes which preserve the isotopy type of the link. Our proof incorporates a result of Lidman and Moore [Trans. Amer. Math. Soc. 369 (2017), pp. 3639–3654] on crossing changes to knots with \n\n \n L\n L\n \n\n-space branched double-covers, as well as tools from Scharlemann and Thompson’s [Comment. Math. Helv. 64 (1989), pp. 527–535] proof of the cosmetic crossing conjecture for the unknot.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the American Mathematical Society, Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/bproc/184","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that a family of links, which includes all special alternating knots, does not admit non-nugatory crossing changes which preserve the isotopy type of the link. Our proof incorporates a result of Lidman and Moore [Trans. Amer. Math. Soc. 369 (2017), pp. 3639–3654] on crossing changes to knots with
L
L
-space branched double-covers, as well as tools from Scharlemann and Thompson’s [Comment. Math. Helv. 64 (1989), pp. 527–535] proof of the cosmetic crossing conjecture for the unknot.
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