A multi-variable Alexander polynomial for a framed transverse graph

Yuanyuan Bao; Zhongtao Wu

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arXiv · 2511.22867

A multi-variable Alexander polynomial for a framed transverse graph

Yuanyuan Bao·Zhongtao Wu

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Abstract

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.

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Yuanyuan Bao, Zhongtao Wu. 2025-11-28. A multi-variable Alexander polynomial for a framed transverse graph. https://arxiv.org/abs/2511.22867

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