Goldman-Turaev formality from the Kontsevitch integral
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916975846883328 |
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| author | Bar-Natan, Dror Dancso, Zsuzsanna Hogan, Tamara Liu, Jessica Scherich, Nancy |
| author_facet | Bar-Natan, Dror Dancso, Zsuzsanna Hogan, Tamara Liu, Jessica Scherich, Nancy |
| contents | We present a new solution to the formality problem for the framed Goldman--Turaev Lie bialgebra, constructing Goldman-Turaev homomorphic expansions (formality isomorphisms) from the Kontsevich integral. Our proof uses a three dimensional derivation of the Goldman-Turaev Lie biaglebra arising from a low-degree Vassiliev quotient -- the {\em emergent} quotient -- of tangles in a thickened punctured disk, modulo a Conway skein relation. This is in contrast to Massuyeau's 2018 proof using braids. A feature of our approach is a general conceptual framework which is applied to prove the compatibility of the homomorphic expansion with both the Goldman bracket and the technically challenging Turaev cobracket. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Goldman-Turaev formality from the Kontsevitch integral Bar-Natan, Dror Dancso, Zsuzsanna Hogan, Tamara Liu, Jessica Scherich, Nancy Quantum Algebra 57K16, 17B62 We present a new solution to the formality problem for the framed Goldman--Turaev Lie bialgebra, constructing Goldman-Turaev homomorphic expansions (formality isomorphisms) from the Kontsevich integral. Our proof uses a three dimensional derivation of the Goldman-Turaev Lie biaglebra arising from a low-degree Vassiliev quotient -- the {\em emergent} quotient -- of tangles in a thickened punctured disk, modulo a Conway skein relation. This is in contrast to Massuyeau's 2018 proof using braids. A feature of our approach is a general conceptual framework which is applied to prove the compatibility of the homomorphic expansion with both the Goldman bracket and the technically challenging Turaev cobracket. |
| title | Goldman-Turaev formality from the Kontsevitch integral |
| topic | Quantum Algebra 57K16, 17B62 |
| url | https://arxiv.org/abs/2509.20983 |