The formality of the Goldman-Turaev Lie bialgebra on a closed surface
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913749178253312 |
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| author | Taniguchi, Toyo |
| author_facet | Taniguchi, Toyo |
| contents | We reformulate the Kashiwara-Vergne groups and associators in higher genera, introduced in Alekseev-Kawazumi-Kuno-Naef, in terms of non-commutative connections using the tools developed in a previous paper. As the main result, the case of closed surfaces is dealt with to determine the pro-unipotent automorphism group of the associated graded of the Goldman-Turaev Lie bialgebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The formality of the Goldman-Turaev Lie bialgebra on a closed surface Taniguchi, Toyo Quantum Algebra Algebraic Topology Geometric Topology Rings and Algebras 57K20 (primary) 17A61, 58B34 (secondary) We reformulate the Kashiwara-Vergne groups and associators in higher genera, introduced in Alekseev-Kawazumi-Kuno-Naef, in terms of non-commutative connections using the tools developed in a previous paper. As the main result, the case of closed surfaces is dealt with to determine the pro-unipotent automorphism group of the associated graded of the Goldman-Turaev Lie bialgebra. |
| title | The formality of the Goldman-Turaev Lie bialgebra on a closed surface |
| topic | Quantum Algebra Algebraic Topology Geometric Topology Rings and Algebras 57K20 (primary) 17A61, 58B34 (secondary) |
| url | https://arxiv.org/abs/2502.06154 |