Superrigidity in infinite dimension and finite rank via harmonic maps
نویسنده
چکیده
We prove geometric superrigidity for actions of cocompact lattices in semisimple Lie groups of higher rank on infinite dimensional Riemannian manifolds of nonpositive curvature and finite telescopic dimension.
منابع مشابه
Infinite dimensional non-positively curved symmetric spaces of finite rank
This paper concerns a study of three families of non-compact type symmetric spaces of infinite dimension. Although they have infinite dimension they have finite rank. More precisely, we show they have finite telescopic dimension. We also show the existence of Furstenberg maps for some group actions on these spaces. Such maps appear as a first step toward superrigidity results.
متن کاملJ ul 2 00 7 SUPERRIGIDITY , GENERALIZED HARMONIC MAPS AND UNIFORMLY CONVEX SPACES
We prove several superrigidity results for isometric actions on Busemann non-positively curved uniformly convex metric spaces. In particular we generalize some recent theorems of N. Monod on uniform and certain non-uniform irreducible lattices in products of locally compact groups, and we give a proof of an unpublished result on commensurability superrigidity due to G.A. Margulis. The proofs re...
متن کاملFe b 20 07 SUPERRIGIDITY , GENERALIZED HARMONIC MAPS AND UNIFORMLY CONVEX SPACES
We prove several superrigidity results for isometric actions on Busemann non-positively curved uniformly convex metric spaces. In particular we generalize some recent theorems of N. Monod on uniform and certain non-uniform irreducible lattices in products of locally compact groups, and we give a proof of an unpublished result on commensurability superrigidity due to G.A. Margulis. The proofs re...
متن کاملSuperrigidity, Generalized Harmonic Maps and Uniformly Convex Spaces
We prove several superrigidity results for isometric actions on Busemann non-positively curved uniformly convex metric spaces. In particular we generalize some recent theorems of N. Monod on uniform and certain non-uniform irreducible lattices in products of locally compact groups, and we give a proof of an unpublished result on commensurability superrigidity due to G.A. Margulis. The proofs re...
متن کاملar X iv : m at h / 06 06 25 6 v 1 [ m at h . G R ] 1 1 Ju n 20 06 SUPERRIGIDITY , GENERALIZED HARMONIC MAPS AND UNIFORMLY CONVEX SPACES
We prove several superrigidity results for isometric actions on metric spaces satisfying some convexity properties. First, we extend some recent theorems of N. Monod on uniform and certain non-uniform irreducible lattices in products of locally compact groups. Second, we include the proof of an unpublished result on commensurability superrigidity due to Margulis. The proofs rely on certain noti...
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