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arXiv · 1210.4030

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

Aurélien Djament·Christine Vespa
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Abstract

We study in this article stable homology of automorphism groups of free groups with coefficients twisted by a poynomial functor. We show that this homology is zero for a reduced covariant polynomial functor. For a reduced contravariant functor, we compute the first homology group, which is in general non zero. Our methods relie on the use of functor categories. ---On étudie dans cet article l'homologie stable des groupes d'automorphismes des groupes libres à coefficients tordus par un foncteur polynomial. On montre que cette homologie est nulle pour un foncteur polynomial covariant réduit. Dans le cas d'un foncteur polynomial réduit contravariant, on calcule le premier groupe d'homologie, qui n'est généralement pas nul. Nos méthodes reposent sur l'utilisation de catégories de foncteurs.

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Aurélien Djament, Christine Vespa. 2013-09-09. Sur l'homologie des groupes d'automorphismes des groupes libres à coefficients polynomiaux. https://arxiv.org/abs/1210.4030

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