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arXiv · 2511.00473

Drinfeld associators and Kashiwara-Vergne associators in higher genera

Toyo Taniguchi
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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 determined from the choice of a Gonzalez-Drinfeld associator, and in the case of genus $1$, we show that only particular framings are realised by our construction.

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Toyo Taniguchi. 2025-11-01. Drinfeld associators and Kashiwara-Vergne associators in higher genera. https://arxiv.org/abs/2511.00473

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