Computation of the centralizer dimension of generalized Baumslag-Solitar groups

A finitely generated group G acting on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag-Solitar group (GBS group). The centralizer dimension of a group G is the maximal length of a descending chain of centralizers. In this paper we complete a description of centralizers for unimodular GBS groups. This allows us to find the centralizer dimension of all GBS groups and to establish a way to compute it.