A topological Tits alternative

Abstract

Let $k$ be a local field, and $\Gamma \leq \mathrm{GL}_{n}(k)$ a linear group over $k$. We prove that $\Gamma $ contains either a relatively open solvable subgroup or a relatively dense free subgroup. This result has applications in dynamics, Riemannian foliations and profinite groups.

Authors

Emmanuel Breuillard

Le centre de mathématiques Laurent Schwartz
Ecole Polytechnique
Palaiseau
France

Tsachik Gelander

Department of Mathematics
The Hebrew University
91904 Jerusalem
Israel