Drinfeld associators and Kashiwara-Vergne associators in higher genera

Fuente: arXiv
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Autore principale: Taniguchi, Toyo
Natura: Preprint
Pubblicazione: 2025
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author Taniguchi, Toyo
author_facet Taniguchi, Toyo
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_00473
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Drinfeld associators and Kashiwara-Vergne associators in higher genera
Taniguchi, Toyo
Quantum Algebra
Algebraic Topology
57K20(primary), 16T05, 16W70, 18M75, 20F36, 20F40, 57M05 (secondary)
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.
title Drinfeld associators and Kashiwara-Vergne associators in higher genera
topic Quantum Algebra
Algebraic Topology
57K20(primary), 16T05, 16W70, 18M75, 20F36, 20F40, 57M05 (secondary)
url https://arxiv.org/abs/2511.00473