Symplectic mapping class groups of blowups of tori

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2023-07-11 DOI:10.1112/topo.12304

Gleb Smirnov

{"title":"Symplectic mapping class groups of blowups of tori","authors":"Gleb Smirnov","doi":"10.1112/topo.12304","DOIUrl":null,"url":null,"abstract":"<p>Let <math>\n <semantics>\n <mi>ω</mi>\n <annotation>$\\omega$</annotation>\n </semantics></math> be a Kähler form on the real 4-torus <math>\n <semantics>\n <msup>\n <mi>T</mi>\n <mn>4</mn>\n </msup>\n <annotation>$T^4$</annotation>\n </semantics></math>. Suppose that <math>\n <semantics>\n <mi>ω</mi>\n <annotation>$\\omega$</annotation>\n </semantics></math> satisfies an irrationality condition that can be achieved by an arbitrarily small perturbation of <math>\n <semantics>\n <mi>ω</mi>\n <annotation>$\\omega$</annotation>\n </semantics></math>. This note shows that the smoothly trivial symplectic mapping class group of the one-point symplectic blowup of <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <msup>\n <mi>T</mi>\n <mn>4</mn>\n </msup>\n <mo>,</mo>\n <mi>ω</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$(T^4,\\omega )$</annotation>\n </semantics></math> is infinitely generated.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12304","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12304","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

Abstract

Let $ω$ be a Kähler form on the real 4-torus $T^{4}$ . Suppose that $ω$ satisfies an irrationality condition that can be achieved by an arbitrarily small perturbation of $ω$ . This note shows that the smoothly trivial symplectic mapping class group of the one-point symplectic blowup of $(T^{4}, ω)$ is infinitely generated.

Abstract Image

查看原文本刊更多论文

复曲面爆破的辛映射类群

设ω$\omega$是实4-环面T4$T^4$上的Kähler形式。假设ω$\omega$满足一个非理性条件，该条件可以通过ω$\omega$的任意小扰动来实现。本文证明了（T4，ω）$（T^4，\omega）$的单点辛爆破的光滑平凡辛映射类群是无限生成的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.