Handlebody Construction of Stein Surfaces
Abstract
Description
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 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 appear
49 pp., AmSTeX, 53 eps figures. Ann. Math., to appear