English

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