{"title":"Lefschetz fibrations with arbitrary signature","authors":"R. Baykur, Noriyuki Hamada","doi":"10.4171/jems/1326","DOIUrl":null,"url":null,"abstract":"We develop techniques to construct explicit symplectic Lefschetz fibrations over the 2-sphere with any prescribed signature and any spin type when the signature is divisible by 16. This solves a long-standing conjecture on the existence of such fibrations with positive signature. As applications, we produce symplectic 4-manifolds that are homeomorphic but not diffeomorphic to connected sums of S^2 x S^2, with the smallest topology known to date, as well as larger examples as symplectic Lefschetz fibrations.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"3 1","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the European Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jems/1326","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
We develop techniques to construct explicit symplectic Lefschetz fibrations over the 2-sphere with any prescribed signature and any spin type when the signature is divisible by 16. This solves a long-standing conjecture on the existence of such fibrations with positive signature. As applications, we produce symplectic 4-manifolds that are homeomorphic but not diffeomorphic to connected sums of S^2 x S^2, with the smallest topology known to date, as well as larger examples as symplectic Lefschetz fibrations.
我们开发了在2球上构造具有任意指定签名和任意自旋类型的显辛Lefschetz纤振的技术，当签名可被16整除时。这就解决了一个长期存在的关于这种具有正特征的振动存在的猜想。作为应用，我们得到了与S^2 x S^2的连通和同胚但不微分同态的辛4流形，具有迄今为止已知的最小拓扑，以及辛Lefschetz纤振等更大的例子。
期刊介绍：
The Journal of the European Mathematical Society (JEMS) is the official journal of the EMS.
The Society, founded in 1990, works at promoting joint scientific efforts between the many different structures that characterize European mathematics. JEMS will publish research articles in all active areas of pure and applied mathematics. These will be selected by a distinguished, international board of editors for their outstanding quality and interest, according to the highest international standards.
Occasionally, substantial survey papers on topics of exceptional interest will also be published. Starting in 1999, the Journal was published by Springer-Verlag until the end of 2003. Since 2004 it is published by the EMS Publishing House. The first Editor-in-Chief of the Journal was J. Jost, succeeded by H. Brezis in 2004.
The Journal of the European Mathematical Society is covered in:
Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.
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