Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (II)

This is the second of a series of papers which give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in a 2-bridge link complement to be homotopic in the link complement. The first paper of the series treated the case of the (2) -bridge torus links. In this paper, we treat the case of (2) -bridge links of slope (n/(2n+1)) and ((n+1)/(3n+2)) , where (n ge 2) is an arbitrary integer.