4流形的多截面

IF 1.2 2区 数学 Q1 MATHEMATICS
Gabriel Islambouli, Patrick Naylor
{"title":"4流形的多截面","authors":"Gabriel Islambouli, Patrick Naylor","doi":"10.1090/tran/8996","DOIUrl":null,"url":null,"abstract":"We introduce multisections of smooth, closed 4-manifolds, which generalize trisections to decompositions with more than three pieces. This decomposition describes an arbitrary smooth, closed 4-manifold as a sequence of cut systems on a surface. We show how to carry out many smooth cut and paste operations in terms of these cut systems. In particular, we show how to implement a cork twist, whereby we show that an arbitrary exotic pair of smooth 4-manifolds admit 4-sections differing only by one cut system. By carrying out fiber sums and log transforms, we also show that the elliptic fibrations <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E left-parenthesis n right-parenthesis Subscript p comma q\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>n</mml:mi> <mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">E(n)_{p,q}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> all admit genus <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=\"application/x-tex\">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> multisections, and draw explicit diagrams for these manifolds.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":" 30","pages":"0"},"PeriodicalIF":1.2000,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Multisections of 4-manifolds\",\"authors\":\"Gabriel Islambouli, Patrick Naylor\",\"doi\":\"10.1090/tran/8996\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce multisections of smooth, closed 4-manifolds, which generalize trisections to decompositions with more than three pieces. This decomposition describes an arbitrary smooth, closed 4-manifold as a sequence of cut systems on a surface. We show how to carry out many smooth cut and paste operations in terms of these cut systems. In particular, we show how to implement a cork twist, whereby we show that an arbitrary exotic pair of smooth 4-manifolds admit 4-sections differing only by one cut system. By carrying out fiber sums and log transforms, we also show that the elliptic fibrations <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper E left-parenthesis n right-parenthesis Subscript p comma q\\\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo stretchy=\\\"false\\\">(</mml:mo> <mml:mi>n</mml:mi> <mml:msub> <mml:mo stretchy=\\\"false\\\">)</mml:mo> <mml:mrow class=\\\"MJX-TeXAtom-ORD\\\"> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">E(n)_{p,q}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> all admit genus <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"3\\\"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=\\\"application/x-tex\\\">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> multisections, and draw explicit diagrams for these manifolds.\",\"PeriodicalId\":23209,\"journal\":{\"name\":\"Transactions of the American Mathematical Society\",\"volume\":\" 30\",\"pages\":\"0\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-11-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the American Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/tran/8996\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the American Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tran/8996","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3

摘要

我们引入光滑、封闭4流形的多截面,将三截面推广到三片以上的分解。这种分解将任意光滑的封闭4流形描述为表面上的一系列切割系统。我们展示了如何根据这些切割系统进行许多平滑的剪切和粘贴操作。特别地,我们展示了如何实现软木扭转,由此我们展示了一个任意的奇异的光滑4流形对承认只有一个切割系统不同的4节。通过纤维和和对数变换,我们还证明了椭圆型纤维E(n) p,q E(n)_{p,q}都允许格33多截面,并绘制了这些流形的显式图。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Multisections of 4-manifolds
We introduce multisections of smooth, closed 4-manifolds, which generalize trisections to decompositions with more than three pieces. This decomposition describes an arbitrary smooth, closed 4-manifold as a sequence of cut systems on a surface. We show how to carry out many smooth cut and paste operations in terms of these cut systems. In particular, we show how to implement a cork twist, whereby we show that an arbitrary exotic pair of smooth 4-manifolds admit 4-sections differing only by one cut system. By carrying out fiber sums and log transforms, we also show that the elliptic fibrations E ( n ) p , q E(n)_{p,q} all admit genus 3 3 multisections, and draw explicit diagrams for these manifolds.
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
来源期刊
CiteScore
2.30
自引率
7.70%
发文量
171
审稿时长
3-6 weeks
期刊介绍: All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信