Tied links in the solid torus

Abstract

We introduce the concept of tied links in the solid torus, which generalizes naturally the concept of tied links in [Formula: see text] previously introduced by Aicardi and Juyumaya. We also define an invariant of these tied links by using skein relations, and we then recover this invariant by using Jones’ method over the bt-algebra of type [Formula: see text] and the Markov trace defined on this.