Strong fillability and the Weinstein conjecture

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 $\Sigma (2,3,6n-1)$, $n\ge 2$, 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.

16 pages, latex2e, no figures, This third version coincides with the second one up to the following generalisation: The Weinstein conjecture holds true for the positively oriented Brieskorn homology spheres $\Sigma (2,3,6n-1)$, $n\ge 2$

References in corpus (2)

• Lectures on open book decompositions and contact structures
• Applications of Hofer's geometry to Hamiltonian dynamics