Goldman-Turaev formality from the Knizhnik-Zamolodchikov connection

Anton Alekseev, Florian Naef

For an oriented 2-dimensional manifold $\Sigma$ of genus $g$ with $n$ boundary components the space $\mathbb{C}{\pi }_1(\Sigma )/[\mathbb{C}{\pi }_1(\Sigma ),\mathbb{C}{\pi }_1(\Sigma )]$ carries the Goldman-Turaev Li…