Quasi-isometric classification of graph manifold groups

Details Quasi-isometric classification of graph manifold groups Quasi-isometric classification of graph manifold groups

2006-04-03

arxiv.org/abs/math/0604042v3

Duke Math. J. 141 (2008), 217--240

Mathematics

Geometric Topology

Revised on referee's comments to add more details in proof. Introduction revised for clarity

Scientific paper

10.1215/S0012-7094-08-14121-3

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.

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