Symplectic cobordisms and the strong Weinstein conjecture
Symplectic Geometry
2019-03-12 v2 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1109.1389,
title = {Symplectic cobordisms and the strong Weinstein conjecture},
author = {Hansjörg Geiges and Kai Zehmisch},
journal= {arXiv preprint arXiv:1109.1389},
year = {2019}
}
Comments
19 pages, 1 figure; v2: several minor changes and corrections