{"title":"论阿诺索夫表征的特征多样性","authors":"Krishnendu Gongopadhyay, Tathagata Nayak","doi":"arxiv-2409.07316","DOIUrl":null,"url":null,"abstract":"Let $\\Gamma$ be the free group $F_n$ of $n$ generators, resp. the fundamental\ngroup $\\pi_1(\\Sigma_g)$ of a closed, connnected, orientatble surface of genus\n$g \\geq 2$. We show that the charater variety of irreducible, resp. Zariski\ndense, Anosov representations of $\\Gamma$ into $\\SL(n, \\C)$ is a complex\nmanifold of (complex) dimension $(n-1)(n^2-1)$, resp. $(2g-2) (n^2-1)$. For\n$\\Gamma=\\pi_1(\\Sigma_g)$, we also show that these character varieties are\nholomorphic symplectic manifolds.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"45 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Character Variety of Anosov Representations\",\"authors\":\"Krishnendu Gongopadhyay, Tathagata Nayak\",\"doi\":\"arxiv-2409.07316\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $\\\\Gamma$ be the free group $F_n$ of $n$ generators, resp. the fundamental\\ngroup $\\\\pi_1(\\\\Sigma_g)$ of a closed, connnected, orientatble surface of genus\\n$g \\\\geq 2$. We show that the charater variety of irreducible, resp. Zariski\\ndense, Anosov representations of $\\\\Gamma$ into $\\\\SL(n, \\\\C)$ is a complex\\nmanifold of (complex) dimension $(n-1)(n^2-1)$, resp. $(2g-2) (n^2-1)$. For\\n$\\\\Gamma=\\\\pi_1(\\\\Sigma_g)$, we also show that these character varieties are\\nholomorphic symplectic manifolds.\",\"PeriodicalId\":501038,\"journal\":{\"name\":\"arXiv - MATH - Representation Theory\",\"volume\":\"45 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Representation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.07316\",\"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 - MATH - Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07316","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let $\Gamma$ be the free group $F_n$ of $n$ generators, resp. the fundamental
group $\pi_1(\Sigma_g)$ of a closed, connnected, orientatble surface of genus
$g \geq 2$. We show that the charater variety of irreducible, resp. Zariski
dense, Anosov representations of $\Gamma$ into $\SL(n, \C)$ is a complex
manifold of (complex) dimension $(n-1)(n^2-1)$, resp. $(2g-2) (n^2-1)$. For
$\Gamma=\pi_1(\Sigma_g)$, we also show that these character varieties are
holomorphic symplectic manifolds.