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

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

2011-06-16

arxiv.org/abs/1106.3156v1

Mathematics

Geometric Topology

Scientific paper

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

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