2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153118Techniques are introduced which determine the geometric structure of non-simple two-generator $3$-manifolds from purely algebraic data. As an application, the satellite knots in the $3$-sphere with a two-generator presentation in which at least one generator is represented by a meridian for the knot are classified.Geometric Topologytext