Hyperbolicity and cubulability are preserved under elementary equivalence

André, Simon

doi:10.2140/gt.2020.24.1075

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Hyperbolicity and cubulability are preserved under elementary equivalence

Simon André

Geometry & Topology 24 (2020) 1075–1147

DOI: 10.2140/gt.2020.24.1075

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

Volume 24, issue 3 (2020)