Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert

Crampon, Mickaël; Marquis, Ludovic

Annales mathématiques Blaise Pascal, Tome 20 (2013), p. 363-376 / Harvested from Numdam

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Résumé
Abstract

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 $x \in Ω$ , 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.

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 $x \in Ω$ , 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.

Publié le : 2013-01-01

MR 3138033 | Zbl 1282.22007 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/ambp.330
Classification: 22E40, 22F50, 57M99
Mots clés: Géométrie de Hilbert, lemme de Margulis, action géométriquement finie

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     author = {Crampon, Micka\"el and Marquis, Ludovic},
     title = {Un lemme de Kazhdan-Margulis-Zassenhaus pour les g\'eom\'etries de Hilbert},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {20},
     year = {2013},
     pages = {363-376},
     doi = {10.5802/ambp.330},
     zbl = {1282.22007},
     mrnumber = {3138033},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AMBP_2013__20_2_363_0}
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Crampon, Mickaël; Marquis, Ludovic. Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert. Annales mathématiques Blaise Pascal, Tome 20 (2013) pp. 363-376. doi : 10.5802/ambp.330. http://gdmltest.u-ga.fr/item/AMBP_2013__20_2_363_0/

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