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2010 On nonseparating contact hypersurfaces in symplectic $4$–manifolds
Peter Albers, Barney Bramham, Chris Wendl
Algebr. Geom. Topol. 10(2): 697-737 (2010). DOI: 10.2140/agt.2010.10.697

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.

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Peter Albers. Barney Bramham. Chris Wendl. "On nonseparating contact hypersurfaces in symplectic $4$–manifolds." Algebr. Geom. Topol. 10 (2) 697 - 737, 2010. https://doi.org/10.2140/agt.2010.10.697

Information

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

zbMATH: 1207.32019
MathSciNet: MR2606798
Digital Object Identifier: 10.2140/agt.2010.10.697

Subjects:
Primary: 32Q65
Secondary: 57R17

Rights: Copyright © 2010 Mathematical Sciences Publishers

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