On Rational Knots and Links in the Solid Torus
  We introduce the notion of rational links in the solid torus. We show that rational links in the solid torus are fully characterized by rational tangles, and hence by the continued fraction of the rational tangle. Furthermore, we generalize this by giving an infinite family of ambient isotopy invariants of colored diagrams in the Kauffman bracket skein module of an oriented surface. 
Khaled Bataineh, Mohamed Elhamdadi, Mustafa Hajij
math.GT