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Quasi-isometric classification of graph manifold groups
Jason A. Behrstock and Walter D. Neumann
Source: Duke Math. J. Volume 141, Number 2 (2008), 217-240.
Abstract
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
Primary Subjects: 20F65
Secondary Subjects: 57N10, 20F36
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1200601791
Digital Object Identifier: doi:10.1215/S0012-7094-08-14121-3
Mathematical Reviews number (MathSciNet):
MR2376814
Zentralblatt MATH identifier:
05237681
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