Amenable hyperbolic groups

Caprace, Pierre-Emmanuel, et al. "Amenable hyperbolic groups." Journal of the European Mathematical Society 017.11 (2015): 2903-2947. <http://eudml.org/doc/277484>.

@article{Caprace2015,
abstract = {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 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.},
author = {Caprace, Pierre-Emmanuel, de Cornulier, Yves, Monod, Nicolas, Tessera, Romain},
journal = {Journal of the European Mathematical Society},
keywords = {Gromov hyperbolic group; locally compact group; amenable group; contracting automorphisms; compacting automorphisms; Gromov hyperbolic group; locally compact group; amenable group; countracting automorphisms; compacting automorphisms},
language = {eng},
number = {11},
pages = {2903-2947},
publisher = {European Mathematical Society Publishing House},
title = {Amenable hyperbolic groups},
url = {http://eudml.org/doc/277484},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Caprace, Pierre-Emmanuel
AU - de Cornulier, Yves
AU - Monod, Nicolas
AU - Tessera, Romain
TI - Amenable hyperbolic groups
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 11
SP - 2903
EP - 2947
AB - 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 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.
LA - eng
KW - Gromov hyperbolic group; locally compact group; amenable group; contracting automorphisms; compacting automorphisms; Gromov hyperbolic group; locally compact group; amenable group; countracting automorphisms; compacting automorphisms
UR - http://eudml.org/doc/277484
ER -