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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. Using this result, we describe all upper‐meridian‐pair‐preserving epimorphisms between 2‐bridge link groups.

Epimorphisms between 2‐bridge link groups: homotopically trivial simple loops on 2‐bridge spheres