Stein fillability and the realization of contact manifolds
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- by C. Denson Hill and Mauro Nacinovich PDF
- Proc. Amer. Math. Soc. 133 (2005), 1843-1850 Request permission
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.References
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Additional Information
- C. Denson Hill
- Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794
- MR Author ID: 211060
- 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
- Received by editor(s): November 19, 2003
- Received by editor(s) in revised form: March 2, 2004
- Published electronically: January 21, 2005
- Communicated by: Jon G. Wolfson
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 1843-1850
- MSC (2000): Primary 53D10, 32V15, 35N99
- DOI: https://doi.org/10.1090/S0002-9939-05-07742-7
- MathSciNet review: 2120286