Wendl, C (2012) Contact Hypersurfaces in Uniruled Symplectic Manifolds Always Separate.
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We observe that nonzero Gromov-Witten invariants with marked point constraints in a closed symplectic manifold imply restrictions on the homology classes that can be represented by contact hypersurfaces. As a special case, contact hypersurfaces must always separate if the symplectic manifold is uniruled. This removes a superfluous assumption in a result of G. Lu, thus implying that all contact manifolds that embed as contact type hypersurfaces into uniruled symplectic manifolds satisfy the Weinstein conjecture.
|Title:||Contact Hypersurfaces in Uniruled Symplectic Manifolds Always Separate|
|Additional information:||8 pages, 1 figure; in v.2 the semipositivity hypothesis has been added, just to be on the safe side|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics|
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