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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.22867 |
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| _version_ | 1866918221796343808 |
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| author | Bao, Yuanyuan Wu, Zhongtao |
| author_facet | Bao, Yuanyuan Wu, Zhongtao |
| contents | We propose a definition of the rotation number for transverse graph diagrams, extending the classical notion of the rotation number for plane curves. Using this, we introduce a normalized multi-variable Alexander polynomial for framed, oriented transverse graphs without sinks or sources, embedded in the 3-sphere $S^3$. We prove that our invariant coincides with the $U_q(\mathfrak{gl}(1\vert 1))$-Alexander polynomial proposed by Viro. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22867 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A multi-variable Alexander polynomial for a framed transverse graph Bao, Yuanyuan Wu, Zhongtao Geometric Topology Primary 57K10 05C10 We propose a definition of the rotation number for transverse graph diagrams, extending the classical notion of the rotation number for plane curves. Using this, we introduce a normalized multi-variable Alexander polynomial for framed, oriented transverse graphs without sinks or sources, embedded in the 3-sphere $S^3$. We prove that our invariant coincides with the $U_q(\mathfrak{gl}(1\vert 1))$-Alexander polynomial proposed by Viro. |
| title | A multi-variable Alexander polynomial for a framed transverse graph |
| topic | Geometric Topology Primary 57K10 05C10 |
| url | https://arxiv.org/abs/2511.22867 |