Superrigidity for irreducible lattices and geometric splitting
Group Theory
2010-01-18 v1 Differential Geometry
Metric Geometry
Abstract
We prove general superrigidity results for actions of irreducible lattices on CAT(0) spaces; first, in terms of the ideal boundary, and then for the intrinsic geometry (including for infinite-dimensional spaces). In particular, one obtains a new and self-contained proof of Margulis' superrigidity theorem for uniform irreducible lattices in non-simple groups. The proofs rely on simple geometric arguments, including a splitting theorem which can be viewed as an infinite-dimensional (and singular) generalization of the Lawson-Yau/Gromoll-Wolf theorem.
Cite
@article{arxiv.math/0504241,
title = {Superrigidity for irreducible lattices and geometric splitting},
author = {Nicolas Monod},
journal= {arXiv preprint arXiv:math/0504241},
year = {2010}
}
Comments
Improved version of earlier preprint. Definitions 3, 5 and proof of Theorem 55 modified