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

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.