{"title":"驯服自同构群的组合","authors":"St'ephane Lamy","doi":"10.5802/afst.1597","DOIUrl":null,"url":null,"abstract":"We study the group Tame($\\mathbf A^3$) of tame automorphisms of the 3-dimensional affine space, over a field of characteristic zero. We recover, in a unified and (hopefully) simplified way, previous results of Kuroda, Shestakov, Umirbaev and Wright, about the theory of reduction and the relations in Tame($\\mathbf A^3$). The novelty in our presentation is the emphasis on a simply connected 2-dimensional simplicial complex on which Tame($\\mathbf A^3$) acts by isometries.","PeriodicalId":122059,"journal":{"name":"Annales de la faculté des sciences de Toulouse Mathématiques","volume":"31 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Combinatorics of the tame automorphism group\",\"authors\":\"St'ephane Lamy\",\"doi\":\"10.5802/afst.1597\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the group Tame($\\\\mathbf A^3$) of tame automorphisms of the 3-dimensional affine space, over a field of characteristic zero. We recover, in a unified and (hopefully) simplified way, previous results of Kuroda, Shestakov, Umirbaev and Wright, about the theory of reduction and the relations in Tame($\\\\mathbf A^3$). The novelty in our presentation is the emphasis on a simply connected 2-dimensional simplicial complex on which Tame($\\\\mathbf A^3$) acts by isometries.\",\"PeriodicalId\":122059,\"journal\":{\"name\":\"Annales de la faculté des sciences de Toulouse Mathématiques\",\"volume\":\"31 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-05-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales de la faculté des sciences de Toulouse Mathématiques\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/afst.1597\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales de la faculté des sciences de Toulouse Mathématiques","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/afst.1597","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
摘要
我们研究了特征为零的域上三维仿射空间的驯服自同构群驯服($\mathbf A^3$)。我们以一种统一的(希望)简化的方式恢复了Kuroda, Shestakov, Umirbaev和Wright先前关于约简理论和Tame($\mathbf a ^3$)中的关系的结果。在我们的演示中，新颖之处在于强调了一个单连通的二维简单复合体，其中Tame($\mathbf a ^3$)通过等距作用。
We study the group Tame($\mathbf A^3$) of tame automorphisms of the 3-dimensional affine space, over a field of characteristic zero. We recover, in a unified and (hopefully) simplified way, previous results of Kuroda, Shestakov, Umirbaev and Wright, about the theory of reduction and the relations in Tame($\mathbf A^3$). The novelty in our presentation is the emphasis on a simply connected 2-dimensional simplicial complex on which Tame($\mathbf A^3$) acts by isometries.
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