Cœur et nombre d'intersection pour les actions de groupes sur les arbres
Combinatorial mapping-torus, branched surfaces and free group automorphisms
We give a characterization of the geometric automorphisms in a certain class of (not necessarily irreducible) free group automorphisms. When the automorphism is geometric, then it is induced by a pseudo-Anosov homeomorphism without interior singularities. An outer free group automorphism is given by a -cocycle of a -complex (a standard dynamical branched surface, see [7] and [9]) the fundamental group of which is the mapping-torus group of the automorphism. A combinatorial construction elucidates...
Commensurations of Out
Let Out(Fn) denote the outer automorphism group of the free group Fn with n>3. We prove that for any finite index subgroup Γ<Out(Fn), the group Aut(Γ) is isomorphic to the normalizer of Γ in Out(Fn). We prove that Γ is co-Hopfian: every injective homomorphism Γ→Γ is surjective. Finally, we prove that the abstract commensurator Comm(Out(Fn)) is isomorphic to Out(Fn).
Conjugacy of subgroups of the general linear group.