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Strong fillability and the Weinstein conjecture

Kai Zehmisch
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Abstract

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 $Σ(2,3,6n-1)$, $n\geq2$, 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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Kai Zehmisch. 2005-04-08. Strong fillability and the Weinstein conjecture. https://arxiv.org/abs/math/0405203

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