On Non-Separating Contact Hypersurfaces in Symplectic 4-Manifolds

Details On Non-Separating Contact Hypersurfaces in Symplectic 4-Manifolds On Non-Separating Contact Hypersurfaces in Symplectic 4-Manifolds

2009-01-07

arxiv.org/abs/0901.0854v3

Algebraic & Geometric Topology (2010), 697-737

Mathematics

Symplectic Geometry

30 pages, 4 figures; v.3 is reorganized somewhat so that the important results are stated sooner and more clearly

Scientific paper

10.2140/agt.2010.10.697

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.

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