- Book学术

发布求助

文献互助智能选刊最新文献

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

{"title":"A note on Stein fillability of circle bundles over symplectic manifolds","authors":"Takahiro Oba","doi":"10.1112/blms.13202","DOIUrl":null,"url":null,"abstract":"We show that, given a closed integral symplectic manifold <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>Σ</mi>\n <mo>,</mo>\n <mi>ω</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$(\\Sigma, \\omega)$</annotation>\n </semantics></math> of dimension <math>\n <semantics>\n <mrow>\n <mn>2</mn>\n <mi>n</mi>\n <mo>⩾</mo>\n <mn>4</mn>\n </mrow>\n <annotation>$2n \\geqslant 4$</annotation>\n </semantics></math>, for every integer <math>\n <semantics>\n <mrow>\n <mi>k</mi>\n <mo>></mo>\n <msub>\n <mo>∫</mo>\n <mi>Σ</mi>\n </msub>\n <msup>\n <mi>ω</mi>\n <mi>n</mi>\n </msup>\n </mrow>\n <annotation>$k>\\int _{\\Sigma }\\omega ^{n}$</annotation>\n </semantics></math>, the Boothby–Wang bundle over <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>Σ</mi>\n <mo>,</mo>\n <mi>k</mi>\n <mi>ω</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$(\\Sigma, k\\omega)$</annotation>\n </semantics></math> 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.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"395-403"},"PeriodicalIF":0.8000,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.13202","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A note on Stein fillability of circle bundles over symplectic manifolds

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.