Two-parabolic-generator subgroups of hyperbolic 3-manifold groups

We give a detailed account of Agol’s theorem and his proof concerning two-meridional-generator subgroups of hyperbolic 2-bridge link groups, which is included in the slide of his talk at the Bolyai conference 2001. We also give a generalization of the theorem to two-parabolic-generator subgroups of hyperbolic 3-manifold groups, which gives a refinement of a result due to Boileau-Weidmann.