Volume 24, issue 3 (2020)

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Hyperbolicity and cubulability are preserved under elementary equivalence

Simon André

Geometry & Topology 24 (2020) 1075–1147
Abstract

The following properties are preserved under elementary equivalence, among finitely generated groups: being hyperbolic (possibly with torsion), being hyperbolic and cubulable, and being a subgroup of a hyperbolic group. In other words, if a finitely generated group G has the same first-order theory as a group possessing one of the previous properties, then G enjoys that property as well.

Keywords
hyperbolic groups, cubulable groups, model theory, elementary equivalence, first-order logic
Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 03C65
References
Publication
Received: 14 February 2018
Revised: 23 April 2019
Accepted: 13 July 2019
Published: 30 September 2020
Proposed: Martin Bridson
Seconded: Anna Wienhard, Walter Neumann
Authors
Simon André
Université de Rennes 1
CNRS
IRMAR-UMR 6625
Rennes
France
Department of Mathematics
Vanderbilt University
Nashville, TN
United States