Stein fillability and the realization of contact manifolds

Hill, C.; Nacinovich, Mauro

doi:10.1090/S0002-9939-05-07742-7

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.

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