Geometry, Topology and Dynamics Seminar
Andres Navas
Universidad de Santiago de Chile
Some remarks on Thurston's stability theorem
Abstract: With no doubt, Thurston's stability theorem is still the most
striking rigidity result for group actions. In this talk I will concentrate on its
1-dimensional version, which establishes that the group of C^1 diffeomorphisms
of the interval is locally indicable (i.e. every finitely generated subgroup surjects
onto Z). I will show by an example that the converse statement does not hold.
More precisely, the semidirect product SL(2,Z) \rtimes Z^2, though locally
indicable (and finitely generated) does not act faithfully by C^1
diffeomorphisms of neither the real line nor the circle. Several
open questions will be addresed.
Wednesday November 18, 2009 at 3:00 PM in SEO 612