Type $C$ skein modules and transparent elements
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916949682814976 |
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| author | Higgins, Vijay Wu, Haihan |
| author_facet | Higgins, Vijay Wu, Haihan |
| contents | We study skein modules using $Sp(2n)$ webs. We define multivariable analogues of Chebyshev polynomials in the Type $C$ setting and use them to construct transparent elements in the skein module at roots of unity. Our arguments are diagrammatic and make use of an explicit braiding formula for $1$ and $k$ labeled strands and an analogue of Kuperberg's tetravalent vertex in the annular setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Type $C$ skein modules and transparent elements Higgins, Vijay Wu, Haihan Geometric Topology Quantum Algebra 57K31, 17B37 We study skein modules using $Sp(2n)$ webs. We define multivariable analogues of Chebyshev polynomials in the Type $C$ setting and use them to construct transparent elements in the skein module at roots of unity. Our arguments are diagrammatic and make use of an explicit braiding formula for $1$ and $k$ labeled strands and an analogue of Kuperberg's tetravalent vertex in the annular setting. |
| title | Type $C$ skein modules and transparent elements |
| topic | Geometric Topology Quantum Algebra 57K31, 17B37 |
| url | https://arxiv.org/abs/2509.11590 |