Đề tài " A topological Tits alternative "

Let k be a local field, and Γ ≤ GLn (k) a linear group over k. We prove that Γ contains either a relatively open solvable subgroup or a relatively dense free subgroup. This result has applications in dynamics, Riemannian foliations and profinite groups. Contents 1. Introduction 2. A generalization of a lemma of Tits 3. Contracting projective transformations 4. Irreducible representations of non-Zariski connected algebraic groups 5. Proof of Theorem in the finitely generated case 6. Dense free subgroups with infinitely many generators 7. Multiple fields, adelic versions and other topologies 8. Applications to profinite groups .

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