{"title":"Curvature distribution and hyperbolicity","authors":"C. Chalk, M. Edjvet","doi":"10.1515/jgth-2022-0106","DOIUrl":null,"url":null,"abstract":"Abstract We describe a method, based on curvature distribution techniques on van Kampen diagrams, for proving finitely presented groups hyperbolic. We apply our method and show that the generalised Fibonacci group F ( r , n ) F(r,n) is hyperbolic when r ≥ 3 r\\geq 3 and n ≥ 6 r + 1 n\\geq 6r+1 and determine which of the groups F ( 3 , n ) F(3,n) are hyperbolic.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jgth-2022-0106","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
Abstract We describe a method, based on curvature distribution techniques on van Kampen diagrams, for proving finitely presented groups hyperbolic. We apply our method and show that the generalised Fibonacci group F ( r , n ) F(r,n) is hyperbolic when r ≥ 3 r\geq 3 and n ≥ 6 r + 1 n\geq 6r+1 and determine which of the groups F ( 3 , n ) F(3,n) are hyperbolic.
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