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A study on foliations, contactstrucures, and symplectic styructures on 3 and 4 dimensional manifolds

3 维和 4 维流形上的叶状结构、接触结构和辛结构的研究

基本信息

批准号：
16540080
负责人：
MITSUMATSU Yoshihiko
金额：
$ 2.37万
依托单位：
Chuo University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540080/
关键词：
foliation contact structure Anosov flow Stein filling spinnable structure symplectic structure Reeb vector field Hamiltonian dynamical system symplectic構造射影的Anosov流 open book分解 Thurston(Bennequin)の不等式

项目摘要

The head Mitsumatsu and an investigator Miyoshi colaborated with others to study the euler class of tangent bundles to foliations and (so called Thurston-Winkelnkemper's) contact structures which are associate with spinnable structures, as a typical class of convergences of contact structures to foliations. Especially they studied the (non-)vanishing of the euler class and the violation of Thurston's inequality and Bennequin's inequlity, from the topological view point of monodromies. As a consequence, a certain class of mapping classes of a surface with boundary can be presented neither as a product of only right-handed Dehn twists nor as that of only right-handed ones. This result was presented in several symposiums including the annual meeting of MSJ in March 2006 as a special invited talk by Miyoshi. The paper is under submission.The investigator Ono studied the symplectec homology from Floer theory as well as from Seiberg-Witten theory. Including the solution to the Flux conjecture as well as the detemination of the symplectic filling of the link of simple singularities, his contributions to this area are profound.The investigator Tsuboi studied the relationship between foliation theory and that of contact structures from the view point of the group of contact diffeomorphisms. The investigator Matsumoto stepped further to the foliation theory and studied the ends of Lie foliations.The head investigator also studied the incompressible fluid dynamics in the framework of the geometry of volume preserving diffeomorphisms and infinite dimensional Hamiltonian systems. He proved that looking from the point of view of such global differential geometry is still valid even to viscous fluides with dissipations. This study is presented in many symposiums, especially as a special project talk in the annual meeting of MSJ in September 2005.

光松和一位研究者三好与其他人合作研究了叶理的切丛的eetan-class和（所谓的Thurston-Winkelnkemper）与可纺结构相关的接触结构，作为一类典型的接触结构收敛到叶理。特别是他们从单值拓扑的角度研究了Escherichia类的（非）消失和Thurston不等式和Bennequin不等式的破坏。因此，有边界曲面的某类映射类既不能表示为仅右手Dehn扭曲的乘积，也不能表示为仅右手Dehn扭曲的乘积。这一结果在几个研讨会上提出，包括2006年3月的MSJ年会，作为Miyoshi的特邀演讲。研究者Ono从Floer理论和Seiberg-Witten理论两个方面研究了辛同调。包括解决的通量猜想以及detemination辛填充的联系简单的奇点，他的贡献，这方面是深刻的。调查坪井研究了叶理理论之间的关系，并认为，接触结构从小组的观点接触的超同态。调查员松本进一步到叶理理论和研究的李叶理的结束。首席调查员还研究了不可压缩流体动力学的框架内的几何体积保持同态和无限维哈密顿系统。他证明，从这个角度来看，这种全球微分几何仍然是有效的，甚至粘性流体dissipatients。这项研究在许多研讨会上提出，特别是在2005年9月的MSJ年会上作为一个特别项目发言。

项目成果

期刊论文数量（32）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

A short note on symplectic Floer theory

关于辛弗洛尔理论的简短说明

DOI：
发表时间：
2005
期刊：
Noncommutative Geometry and Physics
影响因子：
0
作者：
Osaka;N.;小野薫
通讯作者：
小野薫

Convergence of contact structures to foliations, with an Appendix : On Bennequin's isotopy lemma by Y.MITSUMATSU and Atsuhide MORI

接触结构与叶状结构的收敛，附附录：关于 Bennequin 的同位素引理，Y.MITSUMATSU 和 Atsuhide MORI

DOI：
发表时间：
2006
期刊：
Proceedings of Foliation 2005 (to appear)
影响因子：
0
作者：
Shinji Fukuhara;Noriko Yui;Shinji Fukuhara;Shinji Fukuhara;Shinji Fukuhara;Yoshihiko MITSUMATSU;Yoshihiko MITSUMATSU
通讯作者：
Yoshihiko MITSUMATSU

Ends of leaves of Lie foliations

Lie 叶状结构的叶子末端

DOI：
发表时间：
2005
期刊：
J. Math. Soc. Japan 57・3
影响因子：
0
作者：
T.Kobayashi;G.Hector
通讯作者：
G.Hector

Simple Singularities and Symplectic fillings.

简单奇点和辛填充。

DOI：
发表时间：
2005
期刊：
J.Differential.Geom. 69
影响因子：
0
作者：
H.Ohta;K.Ono
通讯作者：
K.Ono

Convergence of contact structures to foliations, with an Appendex : On Bennequin's isotopy lemma by Y. MITSUMATSU and Atsuhide MORI

接触结构与叶状结构的收敛，附附录：关于 Bennequin 的同位素引理，Y. MITSUMATSU 和 Atsuhide MORI

DOI：
发表时间：
2006
期刊：
Proceeding of Foliation 2005 to appear
影响因子：
0
作者：
Shinji Fukuhara;Noriko Yui;Shinji Fukuhara;Shinji Fukuhara;Shinji Fukuhara;Yoshihiko MITSUMATSU
通讯作者：
Yoshihiko MITSUMATSU