Amenable groups that act on the line
Group Theory
2009-07-29 v3 Dynamical Systems
Geometric Topology
Representation Theory
Abstract
Let Gamma be a finitely generated, amenable group. Using an idea of E Ghys, we prove that if Gamma has a nontrivial, orientation-preserving action on the real line, then Gamma has an infinite, cyclic quotient. (The converse is obvious.) This implies that if Gamma has a faithful action on the circle, then some finite-index subgroup of Gamma has the property that all of its nontrivial, finitely generated subgroups have infinite, cyclic quotients. It also means that every left-orderable, amenable group is locally indicable. This answers a question of P Linnell.
Keywords
Cite
@article{arxiv.math/0606232,
title = {Amenable groups that act on the line},
author = {Dave Witte Morris},
journal= {arXiv preprint arXiv:math/0606232},
year = {2009}
}
Comments
This is the version published by Algebraic & Geometric Topology on 15 December 2006