Amenable hyperbolic groups

Details Amenable hyperbolic groups Amenable hyperbolic groups

2012-02-16

arxiv.org/abs/1202.3585v1

Mathematics

Group Theory

40 pages, no figure

Scientific paper

We give a complete characterization of the locally compact groups that are non-elementary 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 semi-regular trees acting doubly transitively on the set of ends. As an application, we show that the class of hyperbolic locally compact groups with a geometrically finite non-uniform lattice, is very restricted.

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