Superrigidity for irreducible lattices and geometric splitting

Abstract

We propose general superrigidity results for actions of irreducible lattices on CAT ( 0 ) spaces. In particular, we obtain a new and self-contained proof of Margulis' superrigidity theorem for uniform irreducible lattices in non-simple groups. However, the statements hold for lattices in products of arbitrary groups; likewise, the geometric representations need not be linear. The proof uses notably a new splitting theorem which can be viewed as an infinite-dimensional and singular generalization of the Lawson–Yau/Gromoll–Wolf theorem. To cite this article: N. Monod, C. R. Acad. Sci. Paris, Ser. I 340 (2005).