2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76671The topology of Stein surfaces and contact 3-manifolds is studied by means of handle decompositions. A simple characterization of homeomorphism types of Stein surfaces is obtained --- they correspond to open handlebodies with all handles of index lessthan or = 2. An uncountable collection of exotic R^4's is shown to admit Stein structures. New invariants of contact 3-manifolds are produced, including a complete (and computable) set of invariants for determining the homotopy class of a 2-plane field on a 3-manifold. These invariants are applicable to Seiberg-Witten theory. Several families of oriented 3-manifolds are examined, namely the Seifert fibered spaces and all surgeries on various links in S^3, and in each case it is seen that ``most'' members of the family are the oriented boundaries of Stein surfaces.49 pp., AmSTeX, 53 eps figures. Ann. Math., to appearGeometric TopologyComplex VariablesDifferential GeometryPrimary 57N13; Secondary 57M50, 57R65, 32C18text