Geometry, Topology and Dynamics Seminar
Dave Morris
University of Lethbridge
Amenable groups that act on the line
Abstract: Let G be a group. It is obvious that if G has an infinite cyclic quotient, then G has a nontrivial action on the real line by orientation-preserving homeomorphisms. The converse is not true in general, but, using an idea of E.Ghys, we prove that the converse does hold for all finitely generated, amenable groups. The proof is surprisingly easy, and combines elementary results from group theory, topology, and the theory of dynamical systems.
Monday April 28, 2008 at 3:00 PM in SEO 612