Some properties of non-positively curved lattices

Pierre-Emmanuel Caprace; Nicolas Monod

doi:10.1016/j.crma.2008.07.006

Geometry

Some properties of non-positively curved lattices

Presented by: Jean-Pierre Demailly

Pierre-Emmanuel Caprace ¹; Nicolas Monod ²

¹ IHES, Le Bois-Marie, 35, rue de Chartres, 91440 Bures-sur-Yvette, France
² EPFL, Ch-1015 Lausanne, Switzerland

Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 857-862.

Abstract
Résumé

We announce results on the structure of CAT(0) groups, CAT(0) lattices and of the underlying spaces. Our statements rely notably on a general study of the full isometry groups of proper CAT(0) spaces. Classical statements about Hadamard manifolds are established for singular spaces; new arithmeticity and rigidity statements are obtained.

Nous présentons des résultats de structure sur les groupes CAT(0), les réseaux CAT(0) et sur les espaces sous-jacents. Nos énoncés reposent notamment sur une étude générale des groupes d'isométries pleins des espaces CAT(0) propres. Nous démontrons des résultats qui généralisent des énoncés classiques sur les variétés de Hadamard et proposons de nouveaux théorèmes d'arithméticité et rigidité.

Received: 2008-05-08
Accepted: 2008-07-03
Published online: 2008-08-01

DOI: 10.1016/j.crma.2008.07.006

Author's affiliations:

Pierre-Emmanuel Caprace ¹; Nicolas Monod ²

¹ IHES, Le Bois-Marie, 35, rue de Chartres, 91440 Bures-sur-Yvette, France
² EPFL, Ch-1015 Lausanne, Switzerland

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Pierre-Emmanuel Caprace; Nicolas Monod. Some properties of non-positively curved lattices. Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 857-862. doi : 10.1016/j.crma.2008.07.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.07.006/

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