Contact Hypersurfaces in Uniruled Symplectic Manifolds Always Separate

Details Contact Hypersurfaces in Uniruled Symplectic Manifolds Always Separate Contact Hypersurfaces in Uniruled Symplectic Manifolds Always Separate

2012-02-21

arxiv.org/abs/1202.4685v1

Mathematics

Symplectic Geometry

8 pages, 1 figure

Scientific paper

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 type hypersurfaces in uniruled symplectic manifolds satisfy the Weinstein conjecture.

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