{"title":"gromov - piatetski - shapiro格同构的细亚群","authors":"Samuel A. Ballas","doi":"10.2140/PJM.2020.309.257","DOIUrl":null,"url":null,"abstract":"In this paper we produce many examples of thin subgroups of special linear groups that are isomorphic to the fundamental groups of non-arithmetic hyperbolic manifolds. Specifically, we show that the non-arithmetic lattices in $\\mathrm{SO}(n,1)$ constructed by Gromov and Piateski-Shapiro can be embedded into $\\mathrm{SL}_{n+1}(\\mathbb{R})$ so that their images are thin subgroups","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Thin subgroups isomorphic to\\nGromov–Piatetski-Shapiro lattices\",\"authors\":\"Samuel A. Ballas\",\"doi\":\"10.2140/PJM.2020.309.257\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we produce many examples of thin subgroups of special linear groups that are isomorphic to the fundamental groups of non-arithmetic hyperbolic manifolds. Specifically, we show that the non-arithmetic lattices in $\\\\mathrm{SO}(n,1)$ constructed by Gromov and Piateski-Shapiro can be embedded into $\\\\mathrm{SL}_{n+1}(\\\\mathbb{R})$ so that their images are thin subgroups\",\"PeriodicalId\":8454,\"journal\":{\"name\":\"arXiv: Geometric Topology\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-11-16\",\"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/10.2140/PJM.2020.309.257\",\"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/10.2140/PJM.2020.309.257","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Thin subgroups isomorphic to
Gromov–Piatetski-Shapiro lattices
In this paper we produce many examples of thin subgroups of special linear groups that are isomorphic to the fundamental groups of non-arithmetic hyperbolic manifolds. Specifically, we show that the non-arithmetic lattices in $\mathrm{SO}(n,1)$ constructed by Gromov and Piateski-Shapiro can be embedded into $\mathrm{SL}_{n+1}(\mathbb{R})$ so that their images are thin subgroups
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