A Kazhdan-Margulis-Zassenhaus lemma for Hilbert geometry

Mickaël Crampon[1]; Ludovic Marquis[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

Annales mathématiques Blaise Pascal (2013)

  • Volume: 20, Issue: 2, page 363-376
  • ISSN: 1259-1734

Abstract

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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 ∈ 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.

How to cite

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Crampon, Mickaël, and Marquis, Ludovic. "Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert." Annales mathématiques Blaise Pascal 20.2 (2013): 363-376. <http://eudml.org/doc/275474>.

@article{Crampon2013,
abstract = {On montre un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert. Plus précisément, en toute dimension $n$, il existe une constante $\varepsilon _n &gt; 0$ telle que, pour tout ouvert proprement convexe $\Omega $, pour tout point $x \in \Omega $, tout groupe discret engendré par un nombre fini d’automorphismes de $\Omega $ qui déplacent le point $x$ de moins de $\varepsilon _n$ est virtuellement nilpotent.},
affiliation = {Universidad de Santiago de Chile, Departamento de Matemática y Ciencia de la Computación, Av. Las Sophoras 173 - Estación Central, Santiago de Chile Chile; IRMAR 263 Av. du Général Leclerc CS 74205 35042 Rennes Cedex France},
author = {Crampon, Mickaël, Marquis, Ludovic},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Hilbert’s geometry; lemma of Margulis; action geometrically finite},
language = {fre},
month = {7},
number = {2},
pages = {363-376},
publisher = {Annales mathématiques Blaise Pascal},
title = {Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert},
url = {http://eudml.org/doc/275474},
volume = {20},
year = {2013},
}

TY - JOUR
AU - Crampon, Mickaël
AU - Marquis, Ludovic
TI - Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert
JO - Annales mathématiques Blaise Pascal
DA - 2013/7//
PB - Annales mathématiques Blaise Pascal
VL - 20
IS - 2
SP - 363
EP - 376
AB - On montre un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert. Plus précisément, en toute dimension $n$, il existe une constante $\varepsilon _n &gt; 0$ telle que, pour tout ouvert proprement convexe $\Omega $, pour tout point $x \in \Omega $, tout groupe discret engendré par un nombre fini d’automorphismes de $\Omega $ qui déplacent le point $x$ de moins de $\varepsilon _n$ est virtuellement nilpotent.
LA - fre
KW - Hilbert’s geometry; lemma of Margulis; action geometrically finite
UR - http://eudml.org/doc/275474
ER -

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