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arXiv · 2105.14497

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

Nariya Kawazumi·Christine Vespa
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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 $\phi: E \to H$ such that $\phi(E)$ is the wheeled PROP generated by the cohomology class h_1 constructed by the first author.

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Nariya Kawazumi, Christine Vespa. 2021-05-30. On the wheeled PROP of stable cohomology of Aut(F_n) with bivariant coefficients. https://doi.org/10.2140/agt.2023.23.3089

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