Drinfeld associators and Kashiwara-Vergne associators in higher genera

Abstract: For $g\geq 0$, a genus $g$ Kashiwara-Vergne associator, introduced by Alekseev-Kawazumi-Kuno-Naef as a solution to the generalised KV equations in relation to the formality problem of the Goldman-Turaev Lie bialgebra on an oriented surface with a framing, is directly constructed from a genus $g$ analogue of a Drinfeld associator formulated by Gonzalez, which we call a Gonzalez-Drinfeld associator. The proof is based on Massuyeau's work in genus 0. The framing is automatically determined from the choice of a Gonzalez-Drinfeld associator, and in the case of genus 1, we show that only one particular framing is realised by our construction.