Duke Mathematical Journal
- Duke Math. J.
- Volume 168, Number 4 (2019), 655-696.
Non-LERFness of arithmetic hyperbolic manifold groups and mixed -manifold groups
We will show that for any noncompact arithmetic hyperbolic -manifold with , and any compact arithmetic hyperbolic -manifold with that is not a -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 -manifold groups. We will also show that a compact orientable irreducible -manifold with empty or tori boundary supports a geometric structure if and only if its fundamental group is LERF.
Duke Math. J., Volume 168, Number 4 (2019), 655-696.
Received: 2 March 2018
Revised: 27 August 2018
First available in Project Euclid: 4 February 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M05: Fundamental group, presentations, free differential calculus
Secondary: 57M05: Fundamental group, presentations, free differential calculus 20E26: Residual properties and generalizations; residually finite groups 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
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