A note on Stein fillability of circle bundles over symplectic manifolds

Takahiro Oba

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arXiv · 2404.14028

A note on Stein fillability of circle bundles over symplectic manifolds

Takahiro Oba

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Abstract

We show that, given a closed integral symplectic manifold $(\Sigma, \omega)$ of dimension $2n \geq 4$, 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.

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Takahiro Oba. 2024-04-22. A note on Stein fillability of circle bundles over symplectic manifolds. https://arxiv.org/abs/2404.14028

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