On the isomorphism problem for generalized Baumslag-Solitar groups: angles

TL;DR

This paper introduces the limit angle, a new dynamical invariant for generalized Baumslag-Solitar groups, enabling classification of certain GBS groups based on geometric behavior.

Contribution

The paper presents the limit angle as a novel invariant that captures geometric interactions, advancing the understanding of GBS group isomorphisms.

Findings

Limit angle is a new invariant for GBS groups.

Classification of GBS groups with one vertex and two edges.

Limit angle reveals geometric behaviors not seen with algebraic invariants.

Abstract

We introduce a new isomorphism invariant for generalized Baumslag-Solitar (GBS) groups, which we call the limit angle. Unlike previously known invariants, which are primarily algebraic, the limit angle admits a dynamical interpretation, arising exclusively in the case of two interacting edges. This invariant captures subtle geometric behavior that does not manifest in configurations with more interacting edges. As an application, we use the limit angle to obtain a classification of GBS groups with one vertex and two edges.