复曲面爆破的辛映射类群

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

Gleb Smirnov

{"title":"复曲面爆破的辛映射类群","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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"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":"{\"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"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\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12304\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12304","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

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。

Symplectic mapping class groups of blowups of tori

查看原文

Symplectic mapping class groups of blowups of tori

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助