The Weinstein conjecture in the presence of submanifolds having a Legendrian foliation

Abstract

Helmut Hofer introduced in '93 a novel technique based on holomorphic curves to prove the Weinstein conjecture. Among the cases where these methods apply are all contact 3--manifolds $(M,\xi )$ with ${\pi }_2(M)\ne 0$. We modify Hofer's argument to prove the Weinstein conjecture for some examples of higher dimensional contact manifolds. In particular, we are able to show that the connected sum with a real projective space always has a closed contractible Reeb orbit.

11 pages, 2 figures

References in corpus (1)

• The plastikstufe - a generalization of the overtwisted disk to higher dimensions

Cited by in corpus (4)

• Gromov compactness for holomorphic discs with totally real boundary conditions
• Symplectic cobordisms and the strong Weinstein conjecture
• Periodic orbits in virtually contact structures
• Higher dimensional contact topology via holomorphic disks