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Commentarii Mathematici Helvetici


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Volume 90, Issue 1, 2015, pp. 33–58
DOI: 10.4171/CMH/345

Published online: 2015-02-23

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

Aurélien Djament[1] and Christine Vespa[2]

(1) Université de Nantes, France
(2) Université de Strasbourg, France

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.

Keywords: Groupes d’automorphismes des groupes libres, homologie des groupes, homologie des foncteurs, foncteurs polynomiaux

Djament Aurélien, Vespa Christine: Sur l’homologie des groupes d’automorphismes des groupes libres à coefficients polynomiaux. Comment. Math. Helv. 90 (2015), 33-58. doi: 10.4171/CMH/345