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