Drinfeld associators and Kashiwara-Vergne associators in higher genera
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915938356428800 |
|---|---|
| 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 |