{"title":"扭环结手术的左序性","authors":"Anh T. Tran","doi":"10.3792/PJAA.95.6","DOIUrl":null,"url":null,"abstract":"We show that the fundamental group of the $3$-manifold obtained by $\\frac{p}{q}$-surgery along the $(n-2)$-twisted $(3,3m+2)$-torus knot, with $n,m \\ge 1$, is not left-orderable if $\\frac{p}{q} \\ge 2n + 6m-3$ and is left-orderable if $\\frac{p}{q}$ is sufficiently close to $0$.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Left-orderability for surgeries on twisted torus knots\",\"authors\":\"Anh T. Tran\",\"doi\":\"10.3792/PJAA.95.6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the fundamental group of the $3$-manifold obtained by $\\\\frac{p}{q}$-surgery along the $(n-2)$-twisted $(3,3m+2)$-torus knot, with $n,m \\\\ge 1$, is not left-orderable if $\\\\frac{p}{q} \\\\ge 2n + 6m-3$ and is left-orderable if $\\\\frac{p}{q}$ is sufficiently close to $0$.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2018-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3792/PJAA.95.6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3792/PJAA.95.6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Left-orderability for surgeries on twisted torus knots
We show that the fundamental group of the $3$-manifold obtained by $\frac{p}{q}$-surgery along the $(n-2)$-twisted $(3,3m+2)$-torus knot, with $n,m \ge 1$, is not left-orderable if $\frac{p}{q} \ge 2n + 6m-3$ and is left-orderable if $\frac{p}{q}$ is sufficiently close to $0$.
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