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Quasi-isometric classification of graph manifold groups. (English) Zbl 1194.20045
Summary: 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

MSC:
20F65 Geometric group theory
57M07 Topological methods in group theory
57N10 Topology of general \(3\)-manifolds (MSC2010)
20F36 Braid groups; Artin groups
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
Software:
nauty
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