On Non-Separating Contact Hypersurfaces in Symplectic 4-Manifolds

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.

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

References in corpus (2)

• Compactness results in Symplectic Field Theory
• Four-dimensional symplectic cobordisms containing three-handles

Cited by in corpus (10)

• Weak and strong fillability of higher dimensional contact manifolds
• A Hierarchy of Local Symplectic Filling Obstructions for Contact 3-Manifolds
• Cylindrical contact homology and topological entropy
• Algebraic Torsion in Contact Manifolds
• Calabi-Yau Caps, Uniruled Caps and Symplectic Fillings
• Symplectic cobordisms and the strong Weinstein conjecture
• Automatic transversality in contact homology II: filtrations and computations
• Contact Hypersurfaces in Uniruled Symplectic Manifolds Always Separate
• Planarity in higher-dimensional contact manifolds
• Homological invariants of codimension 2 contact submanifolds