## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**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

**Time:** 3pm

**Where:** Lunt 105

**Contact Person:** Prof. Keith Burns

**Contact email:** burns@math.northwestern.edu

**Contact Phone:** 847-491-3013

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