{"title":"表示和细三角形的退化","authors":"D. Cooper","doi":"10.1090/conm/760/15287","DOIUrl":null,"url":null,"abstract":"There is a compactification of the space of representations of a finitely generated group into the groups of isometries of all spaces with $\\Delta$-thin triangles. The ideal points are actions on $\\mathbb R$-trees. It is a geometric reformulation and extension of the Culler-Morgan-Shalen theory concerning limits of representations into $\\operatorname{SL}(2,{\\mathbb C})$ and more generally $\\operatorname{O}(n, 1)$. This paper was written and circulated in the early 90's, but never published.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Degenerations of representations and thin\\n triangles\",\"authors\":\"D. Cooper\",\"doi\":\"10.1090/conm/760/15287\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"There is a compactification of the space of representations of a finitely generated group into the groups of isometries of all spaces with $\\\\Delta$-thin triangles. The ideal points are actions on $\\\\mathbb R$-trees. It is a geometric reformulation and extension of the Culler-Morgan-Shalen theory concerning limits of representations into $\\\\operatorname{SL}(2,{\\\\mathbb C})$ and more generally $\\\\operatorname{O}(n, 1)$. This paper was written and circulated in the early 90's, but never published.\",\"PeriodicalId\":8454,\"journal\":{\"name\":\"arXiv: Geometric Topology\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/conm/760/15287\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/conm/760/15287","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Degenerations of representations and thin
triangles
There is a compactification of the space of representations of a finitely generated group into the groups of isometries of all spaces with $\Delta$-thin triangles. The ideal points are actions on $\mathbb R$-trees. It is a geometric reformulation and extension of the Culler-Morgan-Shalen theory concerning limits of representations into $\operatorname{SL}(2,{\mathbb C})$ and more generally $\operatorname{O}(n, 1)$. This paper was written and circulated in the early 90's, but never published.