JournalscmhVol. 90, No. 1pp. 33–58

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

  • Aurélien Djament

    Université de Nantes, France
  • Christine Vespa

    Université de Strasbourg, France
Sur l’homologie des groupes d’automorphismes des groupes libres à coefficients polynomiaux cover
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Abstract

We prove that the stable homology of automorphism groups of free groups with twisted coecients 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 coecients 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.

Cite this article

Aurélien Djament, Christine Vespa, Sur l’homologie des groupes d’automorphismes des groupes libres à coefficients polynomiaux. Comment. Math. Helv. 90 (2015), no. 1, pp. 33–58

DOI 10.4171/CMH/345