Algebraic & Geometric Topology

On nonseparating contact hypersurfaces in symplectic $4$–manifolds

Peter Albers, Barney Bramham, and Chris Wendl

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We show that certain classes of contact 3–manifolds do not admit nonseparating contact type embeddings into any closed symplectic 4–manifold, eg 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–manifold. Similarly, there are symplectic 4–manifolds that can admit smoothly embedded nonseparating hypersurfaces, but not of contact type: we observe that this is the case for all symplectic ruled surfaces.

Article information

Algebr. Geom. Topol., Volume 10, Number 2 (2010), 697-737.

Received: 22 July 2009
Accepted: 5 January 2010
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32Q65: Pseudoholomorphic curves
Secondary: 57R17: Symplectic and contact topology

symplectic manifold contact manifold pseudoholomorphic curve separating hypersurface


Albers, Peter; Bramham, Barney; Wendl, Chris. On nonseparating contact hypersurfaces in symplectic $4$–manifolds. Algebr. Geom. Topol. 10 (2010), no. 2, 697--737. doi:10.2140/agt.2010.10.697.

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