Stabilité homologique pour les groupes d'automorphismes des produits libres

We show in this article that, for any group G indecomposable for the free productand non-isomorphic to Z, the canonical inclusion Aut(Gn ) ! Aut(Gn+1 ) induces an isomorphism between the homology groups Hi for n � 2i + 2, as was conjectured by Hatcher and Wahl. In fact we show a little more — in particular, the result is true for any group G if we replace the automorphism group of the free product by the subgroup of symmetric automorphisms. For this purpose we use constructions and acyclicity results due to McCullough-Miller and Chen-Glover-Jensen and functoriality properties which allow us to apply classical methods in functor homology.