Work

Elementary equivalence vs commensurability for hyperbolic groups

Year: 2017

Type: preprint

Abstract: We study to what extent torsion-free (Gromov)-hyperbolic groups are elementarily equivalent to their finite index subgroups. In particular, we prove that a hyperbolic limit group either is a free product of cyclic groups and surface groups, or admits infinitely many subgroups of finite index which are pairwise non elementarily equivalent.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1701.08853

Authors: Guirardel, Vincent, Levitt, Gilbert, Sklinos, Rizos

Institutions: Centre National de la Recherche Scientifique, Institut de recherche mathématique de Rennes, Université Rennes 1, Université de Rennes, Normandie Université, Laboratoire de Mathématiques Nicolas Oresme, Université de Caen Normandie, Lyon 1 Université, Institut Camille Jordan

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Institut Universitaire de France, Université de Lyon

Awards: G169068394, PROJET AVENIR LYON SAINT-ETIENNE, Community of mathematics and fundamental computer science in Lyon, G4866930200, G6494969328, G7240651115, G7376787254, G7835500200

OpenAlex ID: W2951605666

Cites: 19

Cited by: 2

Related to: 20