Quasi-isometric classification of graph manifold groups

Jason A. Behrstock; Walter D. Neumann

doi:10.1215/s0012-7094-08-14121-3

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Quasi-isometric classification of graph manifold groups

Jason A. Behrstock·Walter D. Neumann

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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.

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BibTeX RIS

Jason A. Behrstock, Walter D. Neumann. 2006-04-03. Quasi-isometric classification of graph manifold groups. https://doi.org/10.1215/s0012-7094-08-14121-3

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