Splittings of generalized Baumslag-Solitar groups

Abstract

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 isomorphism problem for generalized Baumslag-Solitar groups with no non-trivial integral moduli.

20 pages; hyperlinked latex. Version 2: minor changes

References in corpus (2)

• Deformation and rigidity of simplicial group actions on trees
• On uniqueness of JSJ decompositions of finitely generated groups

Cited by in corpus (7)

• On the automorphism group of generalized Baumslag-Solitar groups
• On the isomorphism problem for generalized Baumslag-Solitar groups
• Mapping tori of free group automorphisms, and the Bieri-Neumann-Strebel invariant of graphs of groups
• The Lipschitz metric on deformation spaces of $G$-trees
• C*-algebras associated to graphs of groups
• Incommensurable lattices in Baumslag-Solitar complexes
• Higher-rank GBS groups: non-positive curvature and biautomaticity