## Topology Seminar: The rational Euler characteristic of $Out(F_n)$

Seminar | November 13 | 4:10-5 p.m. | 3 Evans Hall

Karen Vogtmann, University of Warwick

Department of Mathematics

The rational Euler characteristics of many arithmetic groups can be expressed in terms of values of zeta functions, and Harer and Zagier showed that the same is true for surface mapping class groups. J. Smillie and I found a generating function for the rational Euler characteristic of $Out(F_n)$ in 1987. This made computer calculations possible but did not yield qualitative information. I will discuss recent joint work with M. Borinsky that determines the asymptotic behavior and also uncovers a relation with zeta functions.

nickmbmiller@berkeley.edu