Geometry, Topology and Dynamics Seminar
Andres Navas
I.H.E.S. and Univ. of Chile
Groups of circle diffeomorphisms: from algebraic structure to dynamics
Abstract: The goal of this talk is to give the answer in some particular cases to the
question of describing the dynamics of a group of $C^2$ circle diffeomorphisms
using some relevant algebraic information. For instance, this is easy for
the Abelian case, and a classical result by Plante and Thurston reduces
the nilpotent case to this one. The solvable case is more complicated
but can still be completely solved by using simple dynamical methods.
In this direction, the main open problem is the caracterization of
actions of amenable groups.
On the other hand, groups that are too much complicated cannot act on the circle:
finitely generated Kazhdan groups of $C^{3/2}$ circle diffeomorphisms are finite,
and the only higher rank lattices that can act non trivially are those that are
contained in the product of some finite cover of $PSL(2,\mathbb{R})$ with it self.
Friday September 16, 2005 at 3:00 PM in SEO 636