Amenable hyperbolic groups

By P. Caprace, Yves Cornulier, Nicolas Monod, Romain Tessera. 2012

112 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2837abb8e4832eb20c3f887c9f6e1a14db414734

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Metric Geometry of Locally Compact Groups (2014, methodology): “In particular, with the aid of Cayley graphs, Gromov-hyperbolicity makes sense for compactly generated LC-groups, and is invariant by quasi-isometries of these; see for example [CCMT].”
Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces (2013, background): “radial and uniformly radial limit sets of G, respectively. Then (1.2) HD( r) = HD( ur) = :8 The following theorem is a generalization of the Bishop{Jones theorem: 5This terminology was introduced in [19] to describe the cases of a classication of Gromov [37, x3.1]. 6This denition is not equivalent t”