Stein fillability and the realization of contact manifolds
Complex Variables
2007-10-30 v1 Differential Geometry
Symplectic Geometry
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, 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.
Cite
@article{arxiv.0710.5174,
title = {Stein fillability and the realization of contact manifolds},
author = {C. Denson Hill and Mauro Nacinovich},
journal= {arXiv preprint arXiv:0710.5174},
year = {2007}
}