Homogeneity of torsion-free hyperbolic groups

TL;DR

This paper characterizes torsion-free hyperbolic groups that are homogeneous in first-order logic, using JSJ decompositions of their free factors to identify the key structural properties.

Contribution

It provides a complete characterization of homogeneous torsion-free hyperbolic groups based on their JSJ decompositions, linking algebraic structure to logical properties.

Findings

Homogeneous torsion-free hyperbolic groups are characterized by their JSJ decompositions.

The paper establishes a connection between group decompositions and model-theoretic homogeneity.

A classification of such groups is achieved through their free factors' structures.

Abstract

We give a complete characterization of torsion-free hyperbolic groups which are homogeneous in the sense of first-order logic, in terms of the JSJ decompositions of their free factors.