Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert
[A Kazhdan-Margulis-Zassenhaus lemma for Hilbert geometry]
Annales mathématiques Blaise Pascal, Volume 20 (2013) no. 2, pp. 363-376.

We prove a Kazhdan-Margulis-Zassenhaus lemma for Hilbert geometries. More precisely, in every dimension n there exists a constant ε n >0 such that, for any properly convex open set Ω and any point xΩ, any discrete group generated by a finite number of automorphisms of Ω, which displace x at a distance less than ε n , is virtually nilpotent.

On montre un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert. Plus précisément, en toute dimension n, il existe une constante ε n >0 telle que, pour tout ouvert proprement convexe Ω, pour tout point xΩ, tout groupe discret engendré par un nombre fini d’automorphismes de Ω qui déplacent le point x de moins de ε n est virtuellement nilpotent.

DOI: 10.5802/ambp.330
Classification: 22E40,  22F50,  57M99
Keywords: Hilbert’s geometry, lemma of Margulis, action geometrically finite
Crampon, Mickaël 1; Marquis, Ludovic 2

1 Universidad de Santiago de Chile, Departamento de Matemática y Ciencia de la Computación, Av. Las Sophoras 173 - Estación Central, Santiago de Chile Chile
2 IRMAR 263 Av. du Général Leclerc CS 74205 35042 Rennes Cedex France
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Crampon, Mickaël; Marquis, Ludovic. Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert. Annales mathématiques Blaise Pascal, Volume 20 (2013) no. 2, pp. 363-376. doi : 10.5802/ambp.330. http://www.numdam.org/articles/10.5802/ambp.330/

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