A note on Stein fillability of circle bundles over symplectic manifolds

Abstract

We show that, given a closed integral symplectic manifold $(\Sigma ,\omega )$ of dimension $2n\ge 4$, for every integer $k>{\int }_{\Sigma }{\omega }^n$, the Boothby-Wang bundle over $(\Sigma ,k\omega )$ carries no Stein fillable contact structure. This negatively answers a question raised by Eliashberg. A similar result holds for Boothby-Wang orbibundles. As an application, we prove the non-smoothability of some isolated singularities.

9 pages, no figures