{"title":"将R-Fuchsian(4,4,4)三角形群变形为晶格","authors":"Martin Deraux","doi":"10.1016/j.top.2006.06.005","DOIUrl":null,"url":null,"abstract":"<div><p>We prove that the last discrete deformation of the <span><math><mi>R</mi></math></span>-Fuchsian (4, 4, 4)-triangle group in <span><math><mi>P</mi><mi>U</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span> is a cocompact arithmetic lattice. We also describe an experimental method for finding the combinatorics of a Dirichlet fundamental domain, and apply it to the lattice in question.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 6","pages":"Pages 989-1020"},"PeriodicalIF":0.0000,"publicationDate":"2006-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.06.005","citationCount":"29","resultStr":"{\"title\":\"Deforming the R-Fuchsian (4, 4, 4)-triangle group into a lattice\",\"authors\":\"Martin Deraux\",\"doi\":\"10.1016/j.top.2006.06.005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove that the last discrete deformation of the <span><math><mi>R</mi></math></span>-Fuchsian (4, 4, 4)-triangle group in <span><math><mi>P</mi><mi>U</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span> is a cocompact arithmetic lattice. We also describe an experimental method for finding the combinatorics of a Dirichlet fundamental domain, and apply it to the lattice in question.</p></div>\",\"PeriodicalId\":54424,\"journal\":{\"name\":\"Topology\",\"volume\":\"45 6\",\"pages\":\"Pages 989-1020\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.top.2006.06.005\",\"citationCount\":\"29\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0040938306000358\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0040938306000358","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Deforming the R-Fuchsian (4, 4, 4)-triangle group into a lattice
We prove that the last discrete deformation of the -Fuchsian (4, 4, 4)-triangle group in is a cocompact arithmetic lattice. We also describe an experimental method for finding the combinatorics of a Dirichlet fundamental domain, and apply it to the lattice in question.
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