{"title":"曲面基本群的无限表示","authors":"Ryoma Kobayashi","doi":"10.32917/h2022001","DOIUrl":null,"url":null,"abstract":"For any finite type connected surface S, we give an infinite presentation of the fundamental group π1(S,*) of S based at an interior point *∈S whose generators are represented by simple loops. When S is non-orientable, we also give an infinite presentation of the subgroup of π1(S,*) generated by elements which are represented by simple loops whose regular neighborhoods are annuli.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Infinite presentations for fundamental groups of surfaces\",\"authors\":\"Ryoma Kobayashi\",\"doi\":\"10.32917/h2022001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For any finite type connected surface S, we give an infinite presentation of the fundamental group π1(S,*) of S based at an interior point *∈S whose generators are represented by simple loops. When S is non-orientable, we also give an infinite presentation of the subgroup of π1(S,*) generated by elements which are represented by simple loops whose regular neighborhoods are annuli.\",\"PeriodicalId\":55054,\"journal\":{\"name\":\"Hiroshima Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Hiroshima Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32917/h2022001\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hiroshima Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32917/h2022001","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Infinite presentations for fundamental groups of surfaces
For any finite type connected surface S, we give an infinite presentation of the fundamental group π1(S,*) of S based at an interior point *∈S whose generators are represented by simple loops. When S is non-orientable, we also give an infinite presentation of the subgroup of π1(S,*) generated by elements which are represented by simple loops whose regular neighborhoods are annuli.
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.