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15 March 2019 Non-LERFness of arithmetic hyperbolic manifold groups and mixed 3-manifold groups
Hongbin Sun
Duke Math. J. 168(4): 655-696 (15 March 2019). DOI: 10.1215/00127094-2018-0048

Abstract

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.

Citation

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Hongbin Sun. "Non-LERFness of arithmetic hyperbolic manifold groups and mixed 3-manifold groups." Duke Math. J. 168 (4) 655 - 696, 15 March 2019. https://doi.org/10.1215/00127094-2018-0048

Information

Received: 2 March 2018; Revised: 27 August 2018; Published: 15 March 2019
First available in Project Euclid: 4 February 2019

zbMATH: 07055152
MathSciNet: MR3916065
Digital Object Identifier: 10.1215/00127094-2018-0048

Subjects:
Primary: 57M05
Secondary: 20E26, 22E40, 57M05

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 4 • 15 March 2019
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