An Alternative Basis for the Kauffman Bracket Skein Module of the Solid Torus via Braids

Abstract

In this paper we give an alternative basis, Bst, for the Kauffman bracket skein module of the solid torus, KBSM(ST). The basis Bst is obtained with the use of the Tempereley–Lieb algebra of type B and it is appropriate for computing the Kauffman bracket skein module of the lens spaces L(p, q) via braids.