Non-lerfness of arithmetic hyperbolic manifold groups and mixed 3-manifold groups

Jein-Shan Chen Gue Myung Lee Mohamed A Tawhid Hongbin Sun Rutgers University New Brunswick

Geometric Analysis and Geometric Topology mathscidoc:1911.43002

Duke Math Journal, 168, (4), 655–696, 2016
We will show that for any noncompact arithmetic hyperbolic m-manifold with m>3, and any compact arithmetic hyperbolic m-manifold with m > 4 that is not a 7-dimensional one defined by octonions, its fundamental group is not locally extended residually finite (LERF). The main ingredient in the proof is a study on abelian amalgamations of hyperbolic 3-manifold groups. We will also show that a compact orientable irreducible 3-manifold with empty or tori boundary supports a geometric structure if and only if its fundamental group is LERF.
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@inproceedings{jein-shan2016non-lerfness,
  title={NON-LERFNESS OF ARITHMETIC HYPERBOLIC MANIFOLD GROUPS AND MIXED 3-MANIFOLD GROUPS},
  author={Jein-Shan Chen, Gue Myung Lee, Mohamed A Tawhid, and Hongbin Sun},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191110013116481127506},
  booktitle={Duke Math Journal},
  volume={168},
  number={4},
  pages={655–696},
  year={2016},
}
Jein-Shan Chen, Gue Myung Lee, Mohamed A Tawhid, and Hongbin Sun. NON-LERFNESS OF ARITHMETIC HYPERBOLIC MANIFOLD GROUPS AND MIXED 3-MANIFOLD GROUPS. 2016. Vol. 168. In Duke Math Journal. pp.655–696. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191110013116481127506.
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