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

Authors

DOI:

https://doi.org/10.46787/pump.v9i.6333

Keywords:

knots; generating sets; knotted graphs; invariants of knotted graphs

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.

Author Biography

Carmen Caprau , California State University, Fresno

Professor and Department Chair

Department of Mathematics

California State University, Fresno

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Published

2026-01-25

How to Cite

Caprau , C., & Wiest, V. (2026). An Extension of the sl(n) Polynomial to Knotted 4-Valent Graphs. The PUMP Journal of Undergraduate Research, 9, 43–59. https://doi.org/10.46787/pump.v9i.6333

Issue

Vol. 9 (2026): PUMP Journal of Undergraduate Research

Section

Articles

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Copyright (c) 2026 Carmen Caprau , Victoria Wiest

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

The author(s) will retain the copyright, but by submitting the article agree to grant permission to the PUMP Journal of Undergraduate Research to publish, distribute, and archive the article. The author(s) will acknowledge prior publication in the PUMP Journal of Undergraduate Research for all future uses of the article or parts of it.