An Extension of the $sl(n)$ Polynomial to Knotted 4-Valent Graphs

Carmen Caprau; Victoria Wiest

doi:10.46787/pump.v9i.6333

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arXiv · 2601.18144

An Extension of the $sl(n)$ Polynomial to Knotted 4-Valent Graphs

Carmen Caprau·Victoria Wiest

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Abstract

We use planar 4-valent graphs and a graphical calculus involving such graphs to construct an invariant for balanced-oriented, knotted 4-valent graphs. Our invariant is an extension of the $sl(n)$ polynomial for classical knots and links. We also provide a minimal generating set of Reidemeister-type moves for diagrams of balanced-oriented, knotted 4-valent graphs.

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Carmen Caprau, Victoria Wiest. 2026-01-26. An Extension of the $sl(n)$ Polynomial to Knotted 4-Valent Graphs. https://doi.org/10.46787/pump.v9i.6333

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