2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68135We prove results showing that the existence of essential maps of surfaces in a manifold M' obtained from a 3-manifold M by Dehn filling implies the existence of essential maps of surfaces in M.18 pages, 13 figures. To appear Topology and its ApplicationsGeometric Topology57N10; 57M99text