Scaling limits of bipartite planar maps are homeomorphic to the 2-sphere
  We 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. 
J.F. Le Gall, F. Paulin