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1 February 2020 Lattice envelopes
Uri Bader, Alex Furman, Roman Sauer
Duke Math. J. 169(2): 213-278 (1 February 2020). DOI: 10.1215/00127094-2019-0042

Abstract

We introduce a class of countable groups by some abstract group-theoretic conditions. This class includes linear groups with finite amenable radical and finitely generated residually finite groups with some nonvanishing 2-Betti numbers that are not virtually a product of two infinite groups. Further, it includes acylindrically hyperbolic groups. For any group Γ in this class, we determine the general structure of the possible lattice embeddings of Γ, that is, of all compactly generated, locally compact groups that contain Γ as a lattice. This leads to a precise description of possible nonuniform lattice embeddings of groups in this class. Further applications include the determination of possible lattice embeddings of fundamental groups of closed manifolds with pinched negative curvature.

Citation

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Uri Bader. Alex Furman. Roman Sauer. "Lattice envelopes." Duke Math. J. 169 (2) 213 - 278, 1 February 2020. https://doi.org/10.1215/00127094-2019-0042

Information

Received: 13 December 2017; Revised: 31 January 2019; Published: 1 February 2020
First available in Project Euclid: 29 January 2020

zbMATH: 07180377
MathSciNet: MR4057144
Digital Object Identifier: 10.1215/00127094-2019-0042

Subjects:
Primary: 20F65
Secondary: 22D05

Keywords: geometric group theory , lattices , Locally compact groups , quasi-isometries , rigidity

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 2 • 1 February 2020
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