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research article
Amenable hyperbolic groups
We give a complete characterization of the locally compact groups that are nonelementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable subgroup: modulo a compact normal subgroup, these turn out to be either rank one simple Lie groups, or automorphism groups of semiregular trees acting doubly transitively on the set of ends. As an application, we show that the class of hyperbolic locally compact groups with a cusp-uniform nonuniform lattice is very restricted.
Type
research article
Web of Science ID
WOS:000367062100007
Authors
Publication date
2015
Publisher
Published in
Volume
17
Issue
11
Start page
2903
End page
2947
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
February 16, 2016
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