Geodesic
Invariants of $\boldsymbol B$-Type Links via an Extension of the Kauffman Bracket
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 107-130

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In this paper we find a method for constructing solid torus (or: $\boldsymbol B$-type) link invariants by means of extension of the Kauffman bracket for such links. This method can be viewed as the combination of the ideas proposed in [5, 7] and [8] with $\boldsymbol B$-type braid group theoretic approach to solid torus links which is given in [18]. Such method is shown to be compatible with skein relations of $\boldsymbol B$–type and leads to state sum expression for link invariant (in the case of the special diagrams). 
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     author = {P. P. Kulish and A. M. Nikitin},
     title = {Invariants of $\boldsymbol B${-Type} {Links} via an {Extension} of the {Kauffman} {Bracket}},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a7/}
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P. P. Kulish; A. M. Nikitin. Invariants of $\boldsymbol B$-Type Links via an Extension of the Kauffman Bracket. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 107-130. http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a7/