2025/11/01 by Taniguchi, Toyo
#16T05 #16W70 #18M75 #20F36 #20F40 #57K20(primary) #57M05 (secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2511.00473
For g≥ 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.