A note on Stein fillability of circle bundles over symplectic manifolds

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Abstract

We show that, given a closed integral symplectic manifold (, ) of dimension 2n 4, for every integer k>_^n, the Boothby-Wang bundle over (, k) 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 (Mon,) studied this question.

synapsesocial.com/papers/68e6e2eeb6db64358765ebff https://doi.org/https://doi.org/10.48550/arxiv.2404.14028

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