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

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 ϕ : E → H such that ϕ(E) is the wheeled PROP generated by the cohomology class h 1 constructed by the first author.