Symplectic cobordisms and the strong Weinstein conjecture

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.

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

References in corpus (2)

• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• The Weinstein conjecture in the presence of submanifolds having a Legendrian foliation

Cited by in corpus (7)

• Linking and closed orbits
• Polyfolds, Cobordisms, and the strong Weinstein conjecture
• Diffeomorphism type of symplectic fillings of unit cotangent bundles
• Discontinuous symplectic capacities
• Periodic orbits in virtually contact structures
• Finsler geodesics, periodic Reeb orbits, and open books
• Lagrangian non-squeezing and a geometric inequality