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Stein fillability and the realization of contact manifolds

Author(s): C. Denson Hill; Mauro Nacinovich
Journal: Proc. Amer. Math. Soc. 133 (2005), 1843-1850.
MSC (2000): Primary 53D10, 32V15, 35N99
Posted: January 21, 2005
MathSciNet review: 2120286
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Abstract: 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.

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Additional Information:

C. Denson Hill
Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794
Email: dhill@math.sunysb.edu

Mauro Nacinovich
Affiliation: Dipartimento di Matematica, Università di Roma ``Tor Vergata'', via della Ricerca Scientifica, 1 - 00133 - Roma, Italy
Email: nacinovi@mat.uniroma2.it

DOI: 10.1090/S0002-9939-05-07742-7
PII: S 0002-9939(05)07742-7
Keywords: Stein manifold, contact manifold
Received by editor(s): November 19, 2003
Received by editor(s) in revised form: March 2, 2004
Posted: January 21, 2005
Communicated by: Jon G. Wolfson
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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