Mathematical Proceedings of the Cambridge Philosophical Society

Table of Contents - September 2012 - Volume 153, Issue 02  

Research Article

Symplectic cobordisms and the strong Weinstein conjecture

HANSJÖRG GEIGESa1 and KAI ZEHMISCHa1

a1 Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 Köln, Germany. e-mail: geiges@math.uni-koeln.de, kai.zehmisch@math.uni-koeln.de

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.

(Received October 10 2011)

(Revised November 29 2011)

(Online publication February 28 2012)