{"title":"Gluck twisting roll spun knots","authors":"Patrick Naylor, Hannah R. Schwartz","doi":"10.2140/agt.2022.22.973","DOIUrl":null,"url":null,"abstract":"We show that the smooth homotopy 4-sphere obtained by Gluck twisting the m-twist n-roll spin of any unknotting number one knot is diffeomorphic to the standard 4-sphere, for any pair of integers (m,n). It follows as a corollary that an infinite collection of twisted doubles of Gompf's infinite order corks are standard.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"55 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2020-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic and Geometric Topology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/agt.2022.22.973","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 5
Abstract
We show that the smooth homotopy 4-sphere obtained by Gluck twisting the m-twist n-roll spin of any unknotting number one knot is diffeomorphic to the standard 4-sphere, for any pair of integers (m,n). It follows as a corollary that an infinite collection of twisted doubles of Gompf's infinite order corks are standard.
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