Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 10, Number 2 (2010), 697-737.
On nonseparating contact hypersurfaces in symplectic $4$–manifolds
We show that certain classes of contact –manifolds do not admit nonseparating contact type embeddings into any closed symplectic –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 –manifold. Similarly, there are symplectic –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.
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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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