On Non-Separating Contact Hypersurfaces in Symplectic 4-Manifolds
Symplectic Geometry
2010-05-02 v3
Abstract
We show that certain classes of contact 3-manifolds do not admit non-separating contact type embeddings into any closed symplectic 4-manifolds, e.g. this is the case for all contact manifolds that are (partially) planar or have Giroux torsion. The latter implies that manifolds with Giroux torsion do not admit contact type embeddings into any closed symplectic 4-manifolds. Similarly, there are symplectic 4-manifolds that can admit smoothly embedded non-separating hypersurfaces, but not of contact type: we observe that this is the case for all symplectic ruled surfaces.
Cite
@article{arxiv.0901.0854,
title = {On Non-Separating Contact Hypersurfaces in Symplectic 4-Manifolds},
author = {Peter Albers and Barney Bramham and Chris Wendl},
journal= {arXiv preprint arXiv:0901.0854},
year = {2010}
}
Comments
30 pages, 4 figures; v.3 is reorganized somewhat so that the important results are stated sooner and more clearly