Abstract: Drinfeld defined his KZ associator by considering the regularized holonomy of KZ equation along the real interval from 0 to 1 and proved that it satisfies the Pentagon equation. We consider general curves possibly with self intersections and study the equations it satisfied. As an application of this equation, we discuss how to calculate Konstant-Kirilov-Souriou poisson bracket of functions induced by the holonomies of paths on representation space, and the associated graded Goldman bracket, Turaev cobracket of holonomies of loops. The talk is based on arXiv:2402.19138 and a work in progress with Anton Alekseev and Florian Naef.