{"title":"关于汤普森群的几何","authors":"Xavier Martin","doi":"10.1016/S0764-4442(01)02143-7","DOIUrl":null,"url":null,"abstract":"<div><p>Using lambda coordinates from Teichmüller theory, we study the action of the Thompson group <em>T</em> on a relative Teichmüller space, which is defined in terms of piecewise projective homeomorphisms. As an application, we give a geometric interpretation of the homology equivalence between <em>BT</em> and the free loop space <span><math><mtext>L</mtext><mtext>S</mtext><msup><mi></mi><mn>3</mn></msup></math></span>.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 773-778"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02143-7","citationCount":"8","resultStr":"{\"title\":\"Sur la géométrie du groupe de Thompson\",\"authors\":\"Xavier Martin\",\"doi\":\"10.1016/S0764-4442(01)02143-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Using lambda coordinates from Teichmüller theory, we study the action of the Thompson group <em>T</em> on a relative Teichmüller space, which is defined in terms of piecewise projective homeomorphisms. As an application, we give a geometric interpretation of the homology equivalence between <em>BT</em> and the free loop space <span><math><mtext>L</mtext><mtext>S</mtext><msup><mi></mi><mn>3</mn></msup></math></span>.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 8\",\"pages\":\"Pages 773-778\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02143-7\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201021437\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021437","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Using lambda coordinates from Teichmüller theory, we study the action of the Thompson group T on a relative Teichmüller space, which is defined in terms of piecewise projective homeomorphisms. As an application, we give a geometric interpretation of the homology equivalence between BT and the free loop space .
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