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Symplectic cobordisms and the strong Weinstein conjecture

Published online by Cambridge University Press:  28 February 2012

HANSJÖRG GEIGES  and
KAI ZEHMISCH
HANSJÖRG GEIGES
Affiliation:
Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 Köln, Germany. e-mail: geiges@math.uni-koeln.de, kai.zehmisch@math.uni-koeln.de
KAI ZEHMISCH
Affiliation:
Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 Köln, Germany. e-mail: geiges@math.uni-koeln.de, kai.zehmisch@math.uni-koeln.de
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 153 , Issue 2 , September 2012 , pp. 261 - 279
Copyright
Copyright © Cambridge Philosophical Society 2012

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