2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72071Suppose that a three-manifold M contains infinitely many distinct strongly irreducible Heegaard splittings H + nK, obtained by Haken summing the surface H with n copies of the surface K. We show that K is incompressible. All known examples, of manifolds containing infinitely many irreducible Heegaard splittings, are of this form. We also give new examples of such manifolds.30 pages, 22 figuresGeometric Topology57M99text