10/26/2006

Jason Behrstock
University of Utah

Quasi-isometric classification of graph manifolds

We show that the fundamental groups of any two closed irreducible non-geometric graph manifolds are quasi-isometric, resolving a question of Kapovich and Leeb. We also classify the quasi-isometry types of fundamental groups of graph manifolds with boundary in terms of certain finite two-colored graphs. This shows, for instance, that there are exactly 204,535,126 quasi-isometry types of graph manifolds having 8 or fewer Seifert components. Another corollary is a quasi-isometric classification of some families of Artin groups.