Stein fillability and the realization of contact manifolds

There is an intrinsic notion of what it means for a contact manifold to be the smooth boundary of a Stein manifold. The same concept has another more extrinsic formulation, which is often used as a convenient working hypothesis. We give a simple proof that the two are equivalent. Moreover it is show...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2005-06, Vol.133 (6), p.1843-1850
Main Authors: HILL, C. Denson, NACINOVICH, Mauro
Format: Article
Language:English
Subjects:
Coordinate systems
Critical points
Differential geometry
Differential topology
Eigenvalues
Exact sciences and technology
Geometry
Hypersurfaces
Mathematical analysis
Mathematical functions
Mathematical manifolds
Mathematical theorems
Mathematics
Partial differential equations
Sciences and techniques of general use
Several complex variables and analytic spaces
Tangents
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Summary:There is an intrinsic notion of what it means for a contact manifold to be the smooth boundary of a Stein manifold. The same concept has another more extrinsic formulation, which is often used as a convenient working hypothesis. We give a simple proof that the two are equivalent. Moreover it is shown that, even though a border always exists, its germ is not unique; nevertheless the germ of the Dolbeault cohomology of any border is unique. We also point out that any Stein fillable compact contact 3-manifold has a geometric realization in \mathbb{C}^{4} via an embedding, or in \mathbb{C}^{3} via an immersion.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-05-07742-7