2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120061We prove that scaling limits of random planar maps which are uniformly distributed over the set of all rooted 2k-angulations are a.s. homeomorphic to the two-dimensional sphere. Our methods rely on the study of certain random geodesic laminations of the disk.22 pages Second version with minor typographical correctionProbabilityCombinatorics60C05, 05C80text