In this talk I will present the construction of a suitable cube complex X with a G-action, for G a generalized Baumslag-Solitar group BS(p_1, q_1;...;p_n, q_n) = <a, t_1,..., t_n | t_i a^{p_i} = a^{q_i} t_i, t_i t_j = t_j t_i for all i,j>.
Such a complex X is isomorphic to the product of the Bass-Serre trees of the classical BS(p_i, q_i), and by devising an easy-to-check criterion for computing the essential connectivity properties of products of trees (equipped with suitable height functions), the complex can be used to describe the full Σ-theory of the generalized Baumslag-Solitar groups.
This is a joint work with Kevin Klinge and José Pedro Quintanilha
