具有接触奇点的闭辛流形中Fomenko-Zieschang不变量的实现

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2022-01-01 DOI:10.1070/SM9579

D. B. Zot’ev, V. I. Sidel'nikov

{"title":"具有接触奇点的闭辛流形中Fomenko-Zieschang不变量的实现","authors":"D. B. Zot’ev, V. I. Sidel'nikov","doi":"10.1070/SM9579","DOIUrl":null,"url":null,"abstract":"The topological bifurcations of Liouville foliations on invariant -manifolds that are induced by attaching toric -handles are investigated. It is shown that each marked molecule (Fomenko-Zieschang invariant) can be realized on an invariant submanifold of a closed symplectic manifold with contact singularities which is obtained by attaching toric -handles sequentially to a set of symplectic manifolds, while these latter have the structures of locally trivial fibrations over associated with atoms. Bibliography: 10 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"23 1","pages":"443 - 465"},"PeriodicalIF":0.8000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Realization of Fomenko-Zieschang invariants in closed symplectic manifolds with contact singularities\",\"authors\":\"D. B. Zot’ev, V. I. Sidel'nikov\",\"doi\":\"10.1070/SM9579\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The topological bifurcations of Liouville foliations on invariant -manifolds that are induced by attaching toric -handles are investigated. It is shown that each marked molecule (Fomenko-Zieschang invariant) can be realized on an invariant submanifold of a closed symplectic manifold with contact singularities which is obtained by attaching toric -handles sequentially to a set of symplectic manifolds, while these latter have the structures of locally trivial fibrations over associated with atoms. Bibliography: 10 titles.\",\"PeriodicalId\":49573,\"journal\":{\"name\":\"Sbornik Mathematics\",\"volume\":\"23 1\",\"pages\":\"443 - 465\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Sbornik Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1070/SM9579\",\"RegionNum\":4,\"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":"Sbornik Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1070/SM9579","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

研究了由附加环柄引起的不变流形上的Liouville叶的拓扑分岔。证明了每个标记分子(Fomenko-Zieschang不变量)都可以在具有接触奇点的闭辛流形的不变量子流形上实现，该子流形是通过将环柄依次附加到一组辛流形上而得到的，而这些辛流形具有与原子相关的局部平凡颤振结构。参考书目:10篇。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Realization of Fomenko-Zieschang invariants in closed symplectic manifolds with contact singularities

The topological bifurcations of Liouville foliations on invariant -manifolds that are induced by attaching toric -handles are investigated. It is shown that each marked molecule (Fomenko-Zieschang invariant) can be realized on an invariant submanifold of a closed symplectic manifold with contact singularities which is obtained by attaching toric -handles sequentially to a set of symplectic manifolds, while these latter have the structures of locally trivial fibrations over associated with atoms. Bibliography: 10 titles.

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

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis