Duke Mathematical Journal

Non-LERFness of arithmetic hyperbolic manifold groups and mixed $3$-manifold groups

Hongbin Sun

Abstract

We will show that for any noncompact arithmetic hyperbolic $m$-manifold with ${m\gt 3}$, and any compact arithmetic hyperbolic $m$-manifold with $m\gt 4$ 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.

Article information

Source
Duke Math. J., Volume 168, Number 4 (2019), 655-696.

Dates
Revised: 27 August 2018
First available in Project Euclid: 4 February 2019

https://projecteuclid.org/euclid.dmj/1549270813

Digital Object Identifier
doi:10.1215/00127094-2018-0048

Mathematical Reviews number (MathSciNet)
MR3916065

Zentralblatt MATH identifier
07055152

Citation

Sun, Hongbin. Non-LERFness of arithmetic hyperbolic manifold groups and mixed $3$ -manifold groups. Duke Math. J. 168 (2019), no. 4, 655--696. doi:10.1215/00127094-2018-0048. https://projecteuclid.org/euclid.dmj/1549270813

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