{"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":56114,"journal":{"name":"Journal of Topology","volume":"16 3","pages":"877-898"},"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":"{\"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\":\"16 3\",\"pages\":\"877-898\"},\"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}","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}
Symplectic mapping class groups of blowups of tori
Let be a Kähler form on the real 4-torus . Suppose that satisfies an irrationality condition that can be achieved by an arbitrarily small perturbation of . This note shows that the smoothly trivial symplectic mapping class group of the one-point symplectic blowup of is infinitely generated.
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.
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