A topological Tits alternative


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.


Emmanuel Breuillard

Le centre de mathématiques Laurent Schwartz, Ecole Polytechnique, Palaiseau, France

Tsachik Gelander

Department of Mathematics, The Hebrew University, 91904 Jerusalem, Israel