Handlebody Construction of Stein Surfaces

Robert E. Gompf

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arXiv · math/9803019

Handlebody Construction of Stein Surfaces

Robert E. Gompf

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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 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.

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BibTeX RIS

Robert E. Gompf. 1998-03-06. Handlebody Construction of Stein Surfaces. https://arxiv.org/abs/math/9803019

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