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arXiv · 2106.12826

Stable cohomology of graph complexes

Matteo Felder·Florian Naef·Thomas Willwacher
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Abstract

We study three graph complexes related to the higher genus Grothendieck-Teichmüller Lie algebra and diffeomorphism groups of manifolds. We show how the cohomology of these graph complexes is related, and we compute the cohomology as the genus $g$ tends to $\infty$. As a byproduct, we find that the Malcev completion of the genus $g$ mapping class group relative to the symplectic group is Koszul in the stable limit (partially answering a question of Hain). Moreover, we obtain that any elliptic associator gives a solution to the elliptic Kashiwara-Vergne problem.

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Matteo Felder, Florian Naef, Thomas Willwacher. 2021-06-24. Stable cohomology of graph complexes. https://arxiv.org/abs/2106.12826

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