Duke Mathematical Journal

Quasi-isometric classification of graph manifold groups

Jason A. Behrstock and Walter D. Neumann

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We show that the fundamental groups of any two closed irreducible nongeometric graph manifolds are quasi-isometric. 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-isometric classification of Artin groups whose presentation graphs are trees. In particular, any two right-angled Artin groups whose presentation graphs are trees of diameter greater than 2 are quasi-isometric; further, this quasi-isometry class does not include any other right-angled Artin groups

Article information

Duke Math. J., Volume 141, Number 2 (2008), 217-240.

First available in Project Euclid: 17 January 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx] 20F36: Braid groups; Artin groups


Behrstock, Jason A.; Neumann, Walter D. Quasi-isometric classification of graph manifold groups. Duke Math. J. 141 (2008), no. 2, 217--240. doi:10.1215/S0012-7094-08-14121-3. https://projecteuclid.org/euclid.dmj/1200601791

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