S2中的Chekanov环和Gelfand-Zeitlin环 × S2

IF 0.6 4区 数学 Q3 MATHEMATICS
Yoosik Kim
{"title":"S2中的Chekanov环和Gelfand-Zeitlin环 × S2","authors":"Yoosik Kim","doi":"10.1016/j.difgeo.2023.102091","DOIUrl":null,"url":null,"abstract":"<div><p>The Chekanov torus is the first known <em>exotic</em><span><span> torus, a monotone Lagrangian torus that is not </span>Hamiltonian<span> isotopic to the standard monotone Lagrangian torus. We explore the relationship between the Chekanov torus in </span></span><span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and a monotone Lagrangian torus that had been constructed before Chekanov's construction <span>[6]</span>. We prove that the monotone Lagrangian torus fiber in a certain Gelfand–Zeitlin system is related to the Chekanov torus in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> by a symplectomorphism.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Chekanov torus and Gelfand–Zeitlin torus in S2 × S2\",\"authors\":\"Yoosik Kim\",\"doi\":\"10.1016/j.difgeo.2023.102091\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The Chekanov torus is the first known <em>exotic</em><span><span> torus, a monotone Lagrangian torus that is not </span>Hamiltonian<span> isotopic to the standard monotone Lagrangian torus. We explore the relationship between the Chekanov torus in </span></span><span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and a monotone Lagrangian torus that had been constructed before Chekanov's construction <span>[6]</span>. We prove that the monotone Lagrangian torus fiber in a certain Gelfand–Zeitlin system is related to the Chekanov torus in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> by a symplectomorphism.</p></div>\",\"PeriodicalId\":51010,\"journal\":{\"name\":\"Differential Geometry and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-12-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Geometry and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0926224523001171\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224523001171","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

契卡诺夫环是已知的第一个奇异环,一个单调拉格朗日环,它不是标准单调拉格朗日环的哈密顿同位素。我们探讨了S2×S2中的契卡诺夫环面与契卡诺夫构造之前已经构造的单调拉格朗日环面之间的关系[6]。我们用一种复形性证明了某Gelfand-Zeitlin系统中的单调拉格朗日环面纤维与S2×S2中的契卡诺夫环面存在关联。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Chekanov torus and Gelfand–Zeitlin torus in S2 × S2

The Chekanov torus is the first known exotic torus, a monotone Lagrangian torus that is not Hamiltonian isotopic to the standard monotone Lagrangian torus. We explore the relationship between the Chekanov torus in S2×S2 and a monotone Lagrangian torus that had been constructed before Chekanov's construction [6]. We prove that the monotone Lagrangian torus fiber in a certain Gelfand–Zeitlin system is related to the Chekanov torus in S2×S2 by a symplectomorphism.

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
1.00
自引率
20.00%
发文量
81
审稿时长
6-12 weeks
期刊介绍: Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.
×
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