Symplectic cobordisms and the strong Weinstein conjecture

Details Symplectic cobordisms and the strong Weinstein conjecture Symplectic cobordisms and the strong Weinstein conjecture

2011-09-07

arxiv.org/abs/1109.1389v2

Mathematics

Symplectic Geometry

19 pages, 1 figure; v2: several minor changes and corrections

Scientific paper

We study holomorphic spheres in certain symplectic cobordisms and derive information about periodic Reeb orbits in the concave end of these cobordisms from the non-compactness of the relevant moduli spaces. We use this to confirm the strong Weinstein conjecture (predicting the existence of null-homologous Reeb links) for various higher-dimensional contact manifolds, including contact type hypersurfaces in subcritical Stein manifolds and in some cotangent bundles. The quantitative character of this result leads to the definition of a symplectic capacity.

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