Singular links and Yang-Baxter state models (Q501801)

The authors of the paper under review extend the Yang-Baxter state model for the \(sl(n)\)-polynomial [\textit{L. H. Kauffman}, Knots and physics. 3rd ed. Singapore: World Scientific (2001; Zbl 1057.57001)] from classical knots to singular knots and oriented knotted graphs with rigid vertices. The resulting state model is then used to define a representation of the singular braid monoid into a matrix algebra over \(\mathbb{Z}[q^{\pm 1}]\). They also give certain skein relations for planar \(4\)-valent graphs, thus obtaining a polynomial invariant of planar \(4\)-valent graphs using recursive formulas. Their relations seem analogous to the Murakami-Ohtsuki-Yamada [\textit{H. Murakami} et al., Enseign. Math. (2) 44, No. 3--4, 325--360 (1998; Zbl 0958.57014)] state model for the \(sl(n)\)-link invariant.