{"title":"中的扎里斯基密表面子群","authors":"CARMEN GALAZ GARCÍA","doi":"10.1017/s0305004124000070","DOIUrl":null,"url":null,"abstract":"<p>For odd <span>n</span> we construct a path <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325160819198-0562:S0305004124000070:S0305004124000070_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$\\rho\\;:\\;\\thinspace \\Pi_1(S) \\to SL(n\\mathbb{R})$</span></span></img></span></span> of discrete, faithful, and Zariski dense representations of a surface group such that <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325160819198-0562:S0305004124000070:S0305004124000070_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$\\rho_t(\\Pi_1(S)) \\subset SL(n,\\mathbb{Q})$</span></span></img></span></span> for every <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325160819198-0562:S0305004124000070:S0305004124000070_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$t\\in \\mathbb{Q}$</span></span></img></span></span>.</p>","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"32 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Zariski dense surface subgroups in\",\"authors\":\"CARMEN GALAZ GARCÍA\",\"doi\":\"10.1017/s0305004124000070\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>For odd <span>n</span> we construct a path <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325160819198-0562:S0305004124000070:S0305004124000070_inline3.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\rho\\\\;:\\\\;\\\\thinspace \\\\Pi_1(S) \\\\to SL(n\\\\mathbb{R})$</span></span></img></span></span> of discrete, faithful, and Zariski dense representations of a surface group such that <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325160819198-0562:S0305004124000070:S0305004124000070_inline4.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\rho_t(\\\\Pi_1(S)) \\\\subset SL(n,\\\\mathbb{Q})$</span></span></img></span></span> for every <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325160819198-0562:S0305004124000070:S0305004124000070_inline5.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$t\\\\in \\\\mathbb{Q}$</span></span></img></span></span>.</p>\",\"PeriodicalId\":18320,\"journal\":{\"name\":\"Mathematical Proceedings of the Cambridge Philosophical Society\",\"volume\":\"32 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Proceedings of the Cambridge Philosophical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0305004124000070\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Cambridge Philosophical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0305004124000070","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
For odd n we construct a path $\rho\;:\;\thinspace \Pi_1(S) \to SL(n\mathbb{R})$ of discrete, faithful, and Zariski dense representations of a surface group such that $\rho_t(\Pi_1(S)) \subset SL(n,\mathbb{Q})$ for every $t\in \mathbb{Q}$.
期刊介绍：
Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.
$\rho\;:\;\thinspace \Pi_1(S) \to SL(n\mathbb{R})$ of discrete, faithful, and Zariski dense representations of a surface group such that 
$\rho_t(\Pi_1(S)) \subset SL(n,\mathbb{Q})$ for every 
$t\in \mathbb{Q}$.
求助内容：
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