Superrigidity for irreducible lattices and geometric splitting

Details Superrigidity for irreducible lattices and geometric splitting Superrigidity for irreducible lattices and geometric splitting

2005-04-12

arxiv.org/abs/math/0504241v1

See final version in: J. AMS 19 No. 4 (2006) 781--814

Mathematics

Group Theory

Improved version of earlier preprint. Definitions 3, 5 and proof of Theorem 55 modified

Scientific paper

10.1090/S0894-0347-06-00525-X

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.

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