A note on Stein fillability of circle bundles over symplectic manifolds

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-12-06 DOI:10.1112/blms.13202

Takahiro Oba

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Abstract

We show that, given a closed integral symplectic manifold $(Σ, ω)$ of dimension $2 n ⩾ 4$ , for every integer $k > \int_{Σ} ω^{n}$ , the Boothby–Wang bundle over $(Σ, k ω)$ 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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我们证明，给定维数为 2 n ⩾ 4 $2n \geqslant 4$ 的闭积分交点流形 ( Σ , ω ) $(\Sigma, \omega)$ ，对于每一个整数 k >； ∫ Σ ω n $k>int _{\Sigma }\omega ^{n}$，在 ( Σ , k ω ) $(\Sigma, k\omega)$ 上的布斯比-王束不携带斯坦因可填充接触结构。这从反面回答了埃利亚斯伯格提出的一个问题。类似的结果也适用于 Boothby-Wang orbibundles。作为应用，我们证明了一些孤立奇点的非光滑性。

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