Automorphism groups of free, surface, and free abelian groups

Martin R. Bridson and Karen Vogtmann

Preprint, May 2005, modified June 2006 --- to appear in Handbook of Questions around the Mapping Class Group, edited by B.Farb

In this article we describe some of the more striking features of the deep analogy between GL(n,Z),
automorphism groups of free groups, and mapping class groups. Our main purpose is to present a list of
open questions motivated by this analogy.