Invariants of \(B\)-type links via an extension of the Kauffman bracket (Q1405609)

An oriented \(B\)-type link in a solid torus \(M\) can be treated as a mixed link in \(S^3\) containing the complementary solid torus \(I\) since the solid torus \(M\) can be considered as the complement of a solid torus \(I\) in \(S^3\). The classical Alexander and Markov theorems are generalized to the case of \(B\)-type links. The authors also construct invariants of \(B\)-type links generalizing the Kauffman bracket.