A note on Stein fillability of circle bundles over symplectic manifolds

Abstract We show that, given a closed integral symplectic manifold of dimension , for every integer , the Boothby–Wang bundle over 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.