{"title":"一种计算具有一个边界分量的可定向曲面映射类群表示的组合算法","authors":"Lluís Bacardit","doi":"10.1515/gcc-2015-0011","DOIUrl":null,"url":null,"abstract":"Abstract We give an algorithm which computes a presentation for a subgroup, denoted 𝒜ℳ g,p,1 ${\\mathcal {AM}_{g,p,1}}$ , of the automorphism group of a free group. It is known that 𝒜ℳ g,p,1 ${\\mathcal {AM}_{g,p,1}}$ is isomorphic to the mapping class group of an orientable genus-g surface with p punctures and one boundary component. We define a variation of the Auter space.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"74 1","pages":"115 - 95"},"PeriodicalIF":0.1000,"publicationDate":"2010-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A combinatorial algorithm to compute presentations of mapping class groups of orientable surfaces with one boundary component\",\"authors\":\"Lluís Bacardit\",\"doi\":\"10.1515/gcc-2015-0011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We give an algorithm which computes a presentation for a subgroup, denoted 𝒜ℳ g,p,1 ${\\\\mathcal {AM}_{g,p,1}}$ , of the automorphism group of a free group. It is known that 𝒜ℳ g,p,1 ${\\\\mathcal {AM}_{g,p,1}}$ is isomorphic to the mapping class group of an orientable genus-g surface with p punctures and one boundary component. We define a variation of the Auter space.\",\"PeriodicalId\":41862,\"journal\":{\"name\":\"Groups Complexity Cryptology\",\"volume\":\"74 1\",\"pages\":\"115 - 95\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2010-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Groups Complexity Cryptology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/gcc-2015-0011\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Complexity Cryptology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/gcc-2015-0011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
A combinatorial algorithm to compute presentations of mapping class groups of orientable surfaces with one boundary component
Abstract We give an algorithm which computes a presentation for a subgroup, denoted 𝒜ℳ g,p,1 ${\mathcal {AM}_{g,p,1}}$ , of the automorphism group of a free group. It is known that 𝒜ℳ g,p,1 ${\mathcal {AM}_{g,p,1}}$ is isomorphic to the mapping class group of an orientable genus-g surface with p punctures and one boundary component. We define a variation of the Auter space.
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