Title: Pseudo-Anosov dilatations and homology
Speaker: Professor Chris Leininger
Speaker Info: University of Illinois
Brief Description:
Special Note:
Abstract:
The action of a surface homeomorphism F on first homology, or more precisely the logarithm of the leading eigenvalue for the action, provides a lower bound on topological entropy by a theorem of Manning. If F acts trivially on homology, this gives no information. However, in joint work with Benson Farb and Dan Margalit, we prove that if such an F is pseudo-Anosov, then in fact the topological entropy (also equal to the log of its dilatation by a theorem of Fathi and Shub) is at least .098. More generally, we obtain a sequence of positive numbers m(k) tending toward infinity with k, so that if F acts trivially on the quotient of the fundamental group by the k^th term of the lower central series then the log of the dilatation is at least m(k).Date: Tuesday, March 07, 2006