Karen Vogtmann, Cornell University

Abstract:
The standard linear action of GL(n,Z) on n-dimensional Euclidean space R^n induces non-trivial actions of the group Aut(F_n) of automorphisms of a finitely-generated free group on R^n and on the (n-1)-sphere at infinity. We prove that any action of Aut(F_n ) by homeomorphisms on acyclic manifolds or spheres of smaller dimension must be essentially trivial. It follows that any action of SL(n,Z) on such spaces is also trivial. The proof relies on an analysis of the torsion in Aut(F_n) and Smith theory. This is joint work with Martin Bridson.