Strong fillability and the Weinstein conjecture

Details Strong fillability and the Weinstein conjecture Strong fillability and the Weinstein conjecture

2004-05-11

arxiv.org/abs/math/0405203v3

Mathematics

Symplectic Geometry

16 pages, latex2e, no figures, This third version coincides with the second one up to the following generalisation: The Weinst

Scientific paper

Extending work of Chen, we prove the Weinstein conjecture in dimension three for strongly fillable contact structures with either non-vanishing first Chern class or with strong and exact filling having non-trivial canonical bundle. This implies the Weinstein conjecture for certain Stein fillable contact structures obtained by the Eliashberg-Gompf construction.For example we prove the Weinstein conjecture for the Brieskorn homology spheres $\Sigma(2,3,6n-1)$, $n\geq2$, oriented as the boundary of the corresponding Milnor fibre. Furthermore, for tight contact structures on odd lens spaces, non-contractible closed Reeb orbits are found.

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