奇亏格不可定向曲面的映射子群和Dehn扭子群的扭生成集

Pub Date : 2020-07-01 DOI:10.32917/hmj/1595901627
Xiaoming Du
{"title":"奇亏格不可定向曲面的映射子群和Dehn扭子群的扭生成集","authors":"Xiaoming Du","doi":"10.32917/hmj/1595901627","DOIUrl":null,"url":null,"abstract":"A bstract . Let N g be the non-orientable surface of genus g , MCG ð N g Þ the mapping class group of N g , T ð N g Þ the index 2 subgroup generated by all Dehn twists of MCG ð N g Þ . We prove that for odd genus, (1) if g ¼ 4 k þ 3 ð k b 1 Þ , MCG ð N g Þ can be generated by three elements of finite order; (2) if g ¼ 4 k þ 1 ð k b 2 Þ , T ð N g Þ can be generated by three elements of finite order.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"The torsion generating set of the mapping class groups and the Dehn twist subgroups of non-orientable surfaces of odd genus\",\"authors\":\"Xiaoming Du\",\"doi\":\"10.32917/hmj/1595901627\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A bstract . Let N g be the non-orientable surface of genus g , MCG ð N g Þ the mapping class group of N g , T ð N g Þ the index 2 subgroup generated by all Dehn twists of MCG ð N g Þ . We prove that for odd genus, (1) if g ¼ 4 k þ 3 ð k b 1 Þ , MCG ð N g Þ can be generated by three elements of finite order; (2) if g ¼ 4 k þ 1 ð k b 2 Þ , T ð N g Þ can be generated by three elements of finite order.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.32917/hmj/1595901627\",\"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/10.32917/hmj/1595901627","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3

摘要

一个混蛋。让N g属non-orientable地表》成为g, MCGðN g绘图课集团》Þg, TðN gÞ《指数2 subgroup generated by所有Dehn扭曲了的MCGðN gÞ。我们证明那个奇怪的,(1)如果g¼属4 kþ3ðk b 1Þ,MCGðN gÞ可以成为generated byfinite秩序的三个文本;(2)如果g¼4 kþ1,2Þ,Tððk b N gÞ可以成为generated by三个finite命令的文本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
分享
查看原文
The torsion generating set of the mapping class groups and the Dehn twist subgroups of non-orientable surfaces of odd genus
A bstract . Let N g be the non-orientable surface of genus g , MCG ð N g Þ the mapping class group of N g , T ð N g Þ the index 2 subgroup generated by all Dehn twists of MCG ð N g Þ . We prove that for odd genus, (1) if g ¼ 4 k þ 3 ð k b 1 Þ , MCG ð N g Þ can be generated by three elements of finite order; (2) if g ¼ 4 k þ 1 ð k b 2 Þ , T ð N g Þ can be generated by three elements of finite order.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信