The BNS invariants of the generalized solvable Baumslag-Solitar groups and of their finite index subgroups

Splittings of generalized Baumslag–Solitar groups

We study the structure of generalized Baumslag–Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of smallest complexity (fully reduced decompositions) and give a simplified proof of the existence of deformations. We also prove a finiteness theorem and solve the...

A Rigidity Theorem for the Solvable Baumslag-solitar Groups

Solvable Baumslag-solitar Groups Are Not Almost Convex

The arguments of Cannon, Floyd, Grayson and Thurston [CFGT] showing that solvegeometry groups are not almost convex apply to solvable Baumslag-Solitar groups.

C∗-Algebras for Boundary Actions of Solvable Baumslag-Solitar Groups

In this paper we will consider a graph consisting of one vertex and one edge.The Bass-Serre theory gives a tree on which the fundamental group acts. We orient the edge and use this to direct the covering tree. We then consider the action of the fundamental group on the boundary of the directed tree, and study the C∗-algebra of this dynamical system. In this situation the fundamental group is a ...

On the Automorphism Group of Generalized Baumslag-solitar Groups

A generalized Baumslag-Solitar group (GBS group) is a finitely generated group G which acts on a tree with all edge and vertex stabilizers infinite cyclic. We show that Out(G) either contains non-abelian free groups or is virtually nilpotent of class ≤ 2. It has torsion only at finitely many primes. One may decide algorithmically whether Out(G) is virtually nilpotent or not. If it is, one may d...