Sur l'homologie des groupes d'automorphismes des groupes libres \`a coefficients polynomiaux

Aurélien Djament; Christine Vespa

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arXiv · 1210.4030

Sur l'homologie des groupes d'automorphismes des groupes libres \`a 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 \'etudie dans cet article l'homologie stable des groupes d'automorphismes des groupes libres \`a coefficients tordus par un foncteur polynomial. On montre que cette homologie est nulle pour un foncteur polynomial covariant r\'eduit. Dans le cas d'un foncteur polynomial r\'eduit contravariant, on calcule le premier groupe d'homologie, qui n'est g\'en\'eralement pas nul. Nos m\'ethodes reposent sur l'utilisation de cat\'egories de foncteurs.

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Aurélien Djament, Christine Vespa. 2012-10-15. Sur l'homologie des groupes d'automorphismes des groupes libres \`a coefficients polynomiaux. https://arxiv.org/abs/1210.4030

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