{"title":"具有无平方阶循环全局群的紧凑平坦流形基群的无穷属","authors":"Genildo de Jesus Nery","doi":"10.1515/forum-2021-0298","DOIUrl":null,"url":null,"abstract":"In this article, we study the extent to which an <jats:italic>n</jats:italic>-dimensional compact flat manifold with the cyclic holonomy group of square-free order may be distinguished by the finite quotients of its fundamental group. In particular, we display a formula for the cardinality of profinite genus of the fundamental group of an <jats:italic>n</jats:italic>-dimensional compact flat manifold with the cyclic holonomy group of square-free order.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"26 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order\",\"authors\":\"Genildo de Jesus Nery\",\"doi\":\"10.1515/forum-2021-0298\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we study the extent to which an <jats:italic>n</jats:italic>-dimensional compact flat manifold with the cyclic holonomy group of square-free order may be distinguished by the finite quotients of its fundamental group. In particular, we display a formula for the cardinality of profinite genus of the fundamental group of an <jats:italic>n</jats:italic>-dimensional compact flat manifold with the cyclic holonomy group of square-free order.\",\"PeriodicalId\":12433,\"journal\":{\"name\":\"Forum Mathematicum\",\"volume\":\"26 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-01-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Forum Mathematicum\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/forum-2021-0298\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Forum Mathematicum","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/forum-2021-0298","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了具有无平方阶循环全局群的 n 维紧凑平面流形在多大程度上可以通过其基群的有限商来区分。特别是，我们展示了一个具有无平方阶循环全局群的 n 维紧凑平面流形的基群无穷属的心数公式。
Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order
In this article, we study the extent to which an n-dimensional compact flat manifold with the cyclic holonomy group of square-free order may be distinguished by the finite quotients of its fundamental group. In particular, we display a formula for the cardinality of profinite genus of the fundamental group of an n-dimensional compact flat manifold with the cyclic holonomy group of square-free order.
期刊介绍：
Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.
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