Handlebody Construction of Stein Surfaces

1998/03/06 by Robert E. Gompf · 2 citations
Mathematics · #math.GT #math.CV #math.DG #msc:57N13 #msc:57M50 #msc:57R65 #msc:32C18

paper · pdf

published as Ann. Math. 148 (1998), 619-693. · 49 pp., AmSTeX, 53 eps figures. Ann. Math., to appear

arxiv created 1998/03/06 · arxiv updated 2009/11/30

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 lessthan or = 2. An uncountable collection of exotic R⁴'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 S³, and in each case it is seen that ``most'' members of the family are the oriented boundaries of Stein surfaces.

Cited by

• On perturbative invariants of combed three-manifolds
• From Stein manifolds to Oka manifolds: the h-principle in complex analysis

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