Stein fillability and the realization of contact manifolds

Details Stein fillability and the realization of contact manifolds Stein fillability and the realization of contact manifolds

2007-10-26

arxiv.org/abs/0710.5174v1

Proc. AMS 133 (2005), 1843-1850

Mathematics

Complex Variables

Scientific paper

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, it's 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 C^4 via an embedding, or in C^3 via an immersion.

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