Actions of higher-rank lattices on free groups

Abstract

If $G$ is a semisimple Lie group of real rank at least 2 and $\Gamma$ is an irreducible lattice in $G$, then every homomorphism from $\Gamma$ to the outer automorphism group of a finitely generated free group has finite image.

arXiv comment11 pages, no figures. Final version. To appear in Compositio Math