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Comptes Rendus Mathématique
Volume 346, n° 15-16
pages 857-862 (août 2008)
Doi : 10.1016/j.crma.2008.07.006
Received : 8 May 2008 ;  accepted : 3 July 2008
Some properties of non-positively curved lattices
Quelques propriétés des groupes CAT(0)
 

Pierre-Emmanuel Caprace a, 1 , Nicolas Monod b, 2
a IHES, Le Bois-Marie, 35, rue de Chartres, 91440 Bures-sur-Yvette, France 
b EPFL, Ch-1015 Lausanne, Switzerland 

Abstract

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. To cite this article: P.-E. Caprace, N. Monod, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
Résumé

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 dʼisométries 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 dʼarithméticité et rigidité. Pour citer cet article : P.-E. Caprace, N. Monod, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
1  Supported in part by IPDE and a Hodge fellowship.
2  Supported in part by FNS.


© 2008  Published by Elsevier Masson SAS de la part de Académie des sciences.
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