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On nonseparating
contact hypersurfaces in symplectic $4$–manifolds
Peter Albers, Barney Bramham and Chris Wendl |
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Algebraic & Geometric Topology 10 (2010) 697–737
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Abstract |
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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. |
Keywords
symplectic manifold, contact manifold, pseudoholomorphic
curve, separating hypersurface
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Mathematical Subject Classification 2000
Primary: 32Q65
Secondary: 57R17
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References |
Publication
Received: 22 July 2009
Accepted: 5 January 2010
Published: 19 March 2010
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Authors |
| Peter Albers | |
| Department of Mathematics Purdue University 150 N University Street West Lafayette, IN 47907-2067 USA |
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| Barney Bramham | |
| Max-Planck Institut Inselstrasse-22 04103 Leipzig Germany |
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| Chris Wendl | |
| Institut für Mathematik Humboldt-Universität zu Berlin 10099 Berlin Germany |
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