2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62779We prove a structure theorem for 3-manifolds with non-trivial JSJ-decomposition and 2-generated fundamental group. We deduce a variety of Corollaries. Note this is not a complete classification of such manifolds. In particular we believe that one of the families in our list is empty. If you know something about hyperbolic 2-bridge knot exteriors and their finite sheeted covering spaces you might want to finish this off. Thanks.42 pagesGeometric Topologytext