Strong fillability and the Weinstein conjecture
摘要
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 , , 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.
引用
@article{arxiv.math/0405203,
title = {Strong fillability and the Weinstein conjecture},
author = {Kai Zehmisch},
journal= {arXiv preprint arXiv:math/0405203},
year = {2007}
}
备注
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 $\Sigma(2,3,6n-1)$, $n\geq2$