Grothendieck-Teichmüller group and Poisson cohomologies (Q2345698)

It is proven that the Grothendieck-Teichmüller group, \(\mathbf{GRT_1}\), acts up to homotopy on the set \({\pi}\) of Poisson structures on an arbitrary smooth manifold. Universal formulae for such an action can be represented as sums over Feynman graphs with weights given by integrals over compactified configuration spaces. The main purpose of the paper is to study: {\parindent=6mm \begin{itemize}\item[{\(\bullet\)}] a class of universal \(\mathcal Ass_\infty\) structures on \(\mathcal T_{\mathrm{poly}}(\mathbb R^d)\) which are consistent with the Schouten bracket. \item[{\(\bullet\)}] universal actions of the group \(\mathbf{GRT_1}\) on this class. \end{itemize}} The authors study this type of action on Poisson cohomologies of Poisson manifolds, and prove some ``go'' and ``no-go'' theorems associated with these actions.