An Alexander polynomial for MOY graphs

Yuanyuan Bao; Zhongtao Wu

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arXiv · 1708.09092

An Alexander polynomial for MOY graphs

Yuanyuan Bao·Zhongtao Wu

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Abstract

We introduce an Alexander polynomial for MOY graphs. For a framed trivalent MOY graph $\mathbb{G}$, we refine the construction and obtain a framed ambient isotopy invariant $Δ_{(\mathbb{G},c)}(t)$. The invariant $Δ_{(\mathbb{G}, c)}(t)$ satisfies a series of relations, which we call MOY-type relations, and conversely these relations determine $Δ_{(\mathbb{G}, c)}(t)$. Using them we provide a graphical definition of the Alexander polynomial of a link. Finally, we discuss some properties and applications of our invariants.

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BibTeX RIS

Yuanyuan Bao, Zhongtao Wu. 2020-03-30. An Alexander polynomial for MOY graphs. https://arxiv.org/abs/1708.09092

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