{"title":"Twisted Alexander polynomials of $(−2, 3, 2n+1)$-pretzel knots","authors":"Airi Aso","doi":"10.32917/hmj/1583550014","DOIUrl":null,"url":null,"abstract":"We calculate the twisted Alexander polynomials of $(-2,3,2n+1)$-pretzel knots associated to their holonomy representations. As a corollary, we obtain new supporting evidences of Dunfield, Friedl and Jackson's conjecture, that is, the twisted Alexander polynomials of hyperbolic knots associated to their holonomy representations determine the genus and fiberedness of the knots.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2018-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hiroshima Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.32917/hmj/1583550014","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
We calculate the twisted Alexander polynomials of $(-2,3,2n+1)$-pretzel knots associated to their holonomy representations. As a corollary, we obtain new supporting evidences of Dunfield, Friedl and Jackson's conjecture, that is, the twisted Alexander polynomials of hyperbolic knots associated to their holonomy representations determine the genus and fiberedness of the knots.
期刊介绍：
Hiroshima Mathematical Journal (HMJ) is a continuation of Journal of Science of the Hiroshima University, Series A, Vol. 1 - 24 (1930 - 1960), and Journal of Science of the Hiroshima University, Series A - I , Vol. 25 - 34 (1961 - 1970).
Starting with Volume 4 (1974), each volume of HMJ consists of three numbers annually. This journal publishes original papers in pure and applied mathematics. HMJ is an (electronically) open access journal from Volume 36, Number 1.
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