Miraculous cancellations and the quantum Frobenius for $SL_3$ skein modules
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917765695143936 |
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| author | Higgins, Vijay |
| author_facet | Higgins, Vijay |
| contents | We construct a quantum Frobenius map for the $SL_3$ skein module of any oriented 3-manifold specialized at a root of unity, and describe the map by way of threading certain polynomials along links. The homomorphism is a higher rank version of the Chebyshev-Frobenius homomorphism of Bonahon-Wong. The strategy builds on a previous construction of the Frobenius map for $SL_3$ skein algebras of punctured surfaces, using the Frobenius map of Parshall-Wang for the quantum group $\mathcal{O}_q(SL_3).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00351 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Miraculous cancellations and the quantum Frobenius for $SL_3$ skein modules Higgins, Vijay Geometric Topology Quantum Algebra 57K31 We construct a quantum Frobenius map for the $SL_3$ skein module of any oriented 3-manifold specialized at a root of unity, and describe the map by way of threading certain polynomials along links. The homomorphism is a higher rank version of the Chebyshev-Frobenius homomorphism of Bonahon-Wong. The strategy builds on a previous construction of the Frobenius map for $SL_3$ skein algebras of punctured surfaces, using the Frobenius map of Parshall-Wang for the quantum group $\mathcal{O}_q(SL_3).$ |
| title | Miraculous cancellations and the quantum Frobenius for $SL_3$ skein modules |
| topic | Geometric Topology Quantum Algebra 57K31 |
| url | https://arxiv.org/abs/2409.00351 |