Geometry, Topology and Dynamics Seminar
Chris Leininger
UIUC
Title: Pseudo-Anosov dilatations and algebra
Abstract: The dilatation of a pseudo-Anosov homeomorphism F of a closed
surface S_g of genus g is a basic measure of its dynamical complexity.
Penner proved that as g tends to infinity, the logarithm of the smallest
possible dilatation of such a homeomorphism tends to zero on the order of
1/g. I'll discuss joint work with Benson Farb and Dan Margalit that
describes how this type of behavior is prohibited if one imposes certain
algebraic restrictions. As the simplest example, we prove that if F acts
trivially on homology, then the logarithm of its dilatation is bounded
below by .197 (independent of g). I'll also describe how this is sharply
contrasted when one considers a natural measure of topological complexity
in terms of the action on the complex of curves.
Monday May 8, 2006 at 3:00 PM in SEO 512