{"title":"一个亲戚佐佐木集团","authors":"I. Biswas, Mahan Mj","doi":"10.4064/CM8521-3-2021","DOIUrl":null,"url":null,"abstract":"We prove that any one-relator group $G$ is the fundamental group of a compact Sasakian manifold if and only if $G$ is either finite cyclic or isomorphic to the fundamental group of a compact Riemann surface of genus g > 0 with at most one orbifold point of order $n \\geq 1$. We also classify all groups of deficiency at least two that are also the fundamental group of some compact Sasakian manifold.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"One-relator Sasakian groups\",\"authors\":\"I. Biswas, Mahan Mj\",\"doi\":\"10.4064/CM8521-3-2021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that any one-relator group $G$ is the fundamental group of a compact Sasakian manifold if and only if $G$ is either finite cyclic or isomorphic to the fundamental group of a compact Riemann surface of genus g > 0 with at most one orbifold point of order $n \\\\geq 1$. We also classify all groups of deficiency at least two that are also the fundamental group of some compact Sasakian manifold.\",\"PeriodicalId\":49216,\"journal\":{\"name\":\"Colloquium Mathematicum\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-01-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Colloquium Mathematicum\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/CM8521-3-2021\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Colloquium Mathematicum","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/CM8521-3-2021","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
We prove that any one-relator group $G$ is the fundamental group of a compact Sasakian manifold if and only if $G$ is either finite cyclic or isomorphic to the fundamental group of a compact Riemann surface of genus g > 0 with at most one orbifold point of order $n \geq 1$. We also classify all groups of deficiency at least two that are also the fundamental group of some compact Sasakian manifold.
期刊介绍：
Colloquium Mathematicum is a journal devoted to the publication of original papers of moderate length addressed to a broad mathematical audience. It publishes results of original research, interesting new proofs of important theorems and research-expository papers in all fields of pure mathematics.
Two issues constitute a volume, and at least four volumes are published each year.
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