Singular links and Yang-Baxter state models

Abstract

We employ a solution of the Yang-Baxter equation to construct invariants for knot-like objects. Speci\-fically, we consider a Yang-Baxter state model for the {\rm sl($n$)} polynomial of classical links and extend it to oriented singular links and balanced oriented 4-valent knotted graphs with rigid vertices. We also define a representation of the singular braid monoid into a matrix algebra and seek conditions for further extending the invariant to contain topological knotted graphs. In addition, we show that the resulting Yang-Baxter-type invariant for singular links yields a version of the Murakami-Ohtsuki-Yamada state model for the {\rm sl($n$)} polynomial for classical links.