Date/Time
Date(s) - 17/11/2022
3:30 pm - 4:30 pm

Speaker: Michael Borinsky (ETH-ITS Zürich)

Title: Euler characteristics of Out(F_n)

Abstract: I will give an overview on ongoing joint work with Karen Vogtmann on the topology of Out(F_n), the outer automorphism group of the free group of rank n. The first part of this work settled a 1987 conjecture on the virtual Euler characteristic of this family of groups and indicated the existence of many classes in its homology. A similar study has been performed by Harer and Zagier on the virtual Euler characteristic of the mapping class group and the moduli space of curves. I will review a topological field theory proof, due to Kontsevich, of Harer and Zagier’s result and illustrate how an analogous `renormalized’ topological field theory argument can be applied to Out(F_n). Moreover, I will present recent results on the classical Euler characteristic of Out(F_n) and its growth rate which prove the existence of large amounts of unexplained homology in odd dimensions.

Location: HH 312