{"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。
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.