Handlebody Construction of Stein Surfaces

Abstract

The 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 ≤ 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.