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Hyperbolicity and
cubulability are preserved under elementary equivalence
Simon André |
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Geometry & Topology 24 (2020) 1075–1147
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Abstract |
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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 has the same first-order theory as a group possessing one of the previous properties, then enjoys that property as well. |
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Keywords
hyperbolic groups, cubulable groups, model theory,
elementary equivalence, first-order logic
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Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 03C65
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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
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Authors |
| Simon André | |
| Université de Rennes 1 CNRS IRMAR-UMR 6625 Rennes France |
Department of Mathematics Vanderbilt University Nashville, TN United States |
