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.


Published in:
Journal Of The European Mathematical Society, 17, 11, 2903-2947
Year:
2015
Publisher:
Zurich, European Mathematical Soc
ISSN:
1435-9855
Keywords:
Laboratories:




 Record created 2016-02-16, last modified 2018-12-03


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