Quasi-isometric classification of graph manifold groups
Abstract
We show that the fundamental groups of any two closed irreducible non-geometric graph-manifolds are quasi-isometric. This answers 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. A corollary is the quasi-isometry classification of Artin groups whose presentation graphs are trees. In particular any two right-angled Artin groups whose presentation graphs are trees of diameter at least 3 are quasi-isometric, answering a question of Bestvina; further, this quasi-isometry class does not include any other right-angled Artin groups.
Cite
@article{arxiv.math/0604042,
title = {Quasi-isometric classification of graph manifold groups},
author = {Jason A. Behrstock and Walter D. Neumann},
journal= {arXiv preprint arXiv:math/0604042},
year = {2010}
}
Comments
Revised on referee's comments to add more details in proof. Introduction revised for clarity