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arXiv · 1109.1389

Symplectic cobordisms and the strong Weinstein conjecture

Hansjörg Geiges·Kai Zehmisch
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Abstract

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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Hansjörg Geiges, Kai Zehmisch. 2011-11-29. Symplectic cobordisms and the strong Weinstein conjecture. https://doi.org/10.1017/s0305004112000163

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