On the wheeled PROP of stable cohomology of Aut(F_n) with bivariant coefficients

Abstract

We show that the stable cohomology of automorphism groups of free groups with coefficients obtained by applying Hom(-,-) to tensor powers of the abelianization, is equipped with the structure of a wheeled PROP H. We define another wheeled PROP E by Ext-groups in the category of functors from the category of finitely generated free groups to k-modules. The main result of this paper is the construction of a morphism of wheeled PROPs $\varphi :E\to H$ such that $\varphi (E)$ is the wheeled PROP generated by the cohomology class h_1 constructed by the first author.

28 pages

References in corpus (3)

• Cohomological Aspects of Magnus Expansions
• Cohomologie des foncteurs polynomiaux sur les groupes libres
• Twisted Morita-Mumford classes on braid groups

Cited by in corpus (1)

• Stable cohomology of $Aut(F_n)$ with bivariant twisted coefficients