Geometry, Topology and Dynamics Seminar
Steve Hurder
UIC
Exceptional minimal sets and the Godbillon-Vey class
Abstract: We consider a C^2 action of a countable group G on the circle, and prove the following Theorem: The
set of infinitesimally expansive points in an exceptional minimal set has Lebesgue measure zero. The
proof introduces a new technique using "uniform expanders" and points of Lebesgue density one.
This result has a nice application: the Godbillon-Vey class GV(F) of a foliation F with a complete
transverse circle vanishes on an exceptional minimal set. This answers a question posed by
Matsumoto in 1985. Hence, the class GV(F) non-zero implies the foliation has an open local minimal
set. The associated holonomy group action on the transverse circle must have an open local minimal
set containing a resilient orbit.
Monday August 29, 2005 at 3:00 PM in SEO 512