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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On nonseparating contact hypersurfaces in symplectic $4$–manifolds

Peter Albers, Barney Bramham and Chris Wendl

Algebraic & Geometric Topology 10 (2010) 697–737
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.

Keywords
symplectic manifold, contact manifold, pseudoholomorphic curve, separating hypersurface
Mathematical Subject Classification 2000
Primary: 32Q65
Secondary: 57R17
References
Publication
Received: 22 July 2009
Accepted: 5 January 2010
Published: 19 March 2010
Authors
Peter Albers
Department of Mathematics
Purdue University
150 N University Street
West Lafayette, IN 47907-2067
USA
Barney Bramham
Max-Planck Institut
Inselstrasse-22
04103 Leipzig
Germany
Chris Wendl
Institut für Mathematik
Humboldt-Universität zu Berlin
10099 Berlin
Germany