Epimorphisms between 2-bridge link groups: Homotopically trivial simple loops on 2-bridge spheres

We give a complete characterization of those essential simple loops on 2-bridge spheres of 2-bridge links which are null-homotopic in the link complements. By using this result, we describe all upper-meridian-pair-preserving epimorphisms between 2-bridge link groups.Comment: 39 pages, 4 figures; updated version, incorporating the referee's comments; to appear in Proceedings of the London Mathematical Societ