## Algebraic & Geometric Topology

### On nonseparating contact hypersurfaces in symplectic $4$–manifolds

#### Abstract

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

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

Dates
Accepted: 5 January 2010
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715112

Digital Object Identifier
doi:10.2140/agt.2010.10.697

Mathematical Reviews number (MathSciNet)
MR2606798

Zentralblatt MATH identifier
1207.32019

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

#### Citation

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. https://projecteuclid.org/euclid.agt/1513715112

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