The 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 1.3 in the finitely generated case 6. Dense free subgroups with infinitely many generators 7.

49p noel_noel 17-01-2013 56 8   Download

This is the second of two papers in which we prove the Tits alternative for Out(Fn ). Contents 1. Introduction and outline 2. Fn -trees 2.1. Real trees 2.2. Real Fn -trees 2.3. Very small trees 2.4. Spaces of real Fn -trees 2.5. Bounded cancellation constants 2.6. Real graphs 2.7. Models and normal forms for simplicial Fn -trees 2.8. Free factor systems 3. Unipotent polynomially growing outer automorphisms 3.1. Unipotent linear maps 3.2. Topological representatives 3.3. Relative train tracks and automorphisms of polynomial growth 3.4. Unipotent representatives and UPG automorphisms ...

60p noel_noel 17-01-2013 45 5   Download