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On nonseparating contact hypersurfaces in symplectic 4–manifolds

Peter Albers, Barney Bramham, Chris Wendl
2010 Algebraic and Geometric Topology  
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
more » ... , but not of contact type: we observe that this is the case for all symplectic ruled surfaces.
doi:10.2140/agt.2010.10.697 fatcat:jkmgba3juvawrjn2xskyx3v4vy