Sur l’homologie des groupes d’automorphismes des groupes libres à coefficients polynomiaux

Abstract

We prove that the stable homology of automorphism groups of free groups with twisted coefficients given by a polynomial covariant functor is trivial. For the abelianization functor, which is polynomial of degree 1, we recover by algebraic methods a result previously obtained by Hatcher–Wahl by topological and geometrical methods. For coefficients given by a contravariant polynomial functor factorizing through the abelianization, we compute the stable value of the first homology group of automorphism groups of free groups, which is generally nonzero.