2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220684It was proved by H. Whitney in 1933 that a Serre fibration of compact metric spaces admits a global section provided every fiber is homeomorphic to the unit interval [0,1]. An extension of the Whitney's theorem to the case when all fibers are homeomorphic to some fixed compact two-dimensional manifold was proved by the authors \cite{BCS}. The main result of this paper proves the existence of local sections in a Serre fibration with all fibers homeomorphic to some fixed compact three-dimensional manifold.Submitted to Topolofy and its ApplicationsGeometric TopologyGeneral Topology57N05, 57N10, 54C65text