2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121708We give a proof of the so-called generalized Waldhausen conjecture, which says that an orientable irreducible atoroidal 3-manifold has only finitely many Heegaard splittings in each genus, up to isotopy. Jaco and Rubinstein have announced a proof of this conjecture using different methods.Geometric Topology57M50; 57N10; 57M25text