Open books and the Weinstein conjecture

Abstract

We show the existence of a contractible periodic Reeb orbit for any contact structure supported by an open book whose binding can be realised as a hypersurface of restricted contact type in a subcritical Stein manifold. A key ingredient in the proof is a higher-dimensional version of Eliashberg's theorem about symplectic cobordisms from a contact manifold to a symplectic fibration.

16 pages, 2 figures

References in corpus (1)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures

Cited by in corpus (12)

• Contact homology and virtual fundamental cycles
• On symplectic fillings of spinal open book decompositions I: Geometric constructions
• Polyfolds, Cobordisms, and the strong Weinstein conjecture
• On some examples and constructions of contact manifolds
• Periodic orbits in virtually contact structures
• Generalizations of planar contact manifolds to higher dimensions
• Finsler geodesics, periodic Reeb orbits, and open books
• Planarity in higher-dimensional contact manifolds
• Contact open books with flexible pages
• Cobordisms between symplectic fibrations
• Homological invariants of codimension 2 contact submanifolds
• Open books and exact symplectic cobordisms