Synthetic Studies ofTopology

拓扑综合研究

• 批准号: 17204007
• 负责人: MATSUMOTO Shigenori
• 金额: $ 29.12万
• 依托单位: Nihon University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17204007/
• 关键词: manifold; roun action; dynamical systems; manning class group; hyperbolic space; homotopv group; singularity; foliation; 写像類群; 結び目

Recent progress of topology is prompted by the recognition of its relationship with the other area of mathematics which includes differential Geometry, algebra, analysis and mathematical physics. This makes the method of investigation more sophisticated and gives the researches wider perspectives. The purpose of this research project is to make cooperation of various researchers easy and timingly, making the field more active .We have successfully maintained the network of topologists, organized various symposia and conferences timingly, did exchanges of the researchers, invited various well recognized foreign researchers, gave many colloquia abroad, thus contributing to the development of topology in a significant way.Concretely the research of the following areas of topology is developed by our research projects: Theory of singularities of algebraic and differentiable maps: Group actions on manifolds and on simplicial complexes: Actions of mapping class groups on Teichmuller spaces of the surface: Theory of dynamical systems of complex analytic maps: Dynamical study of vector fields on manifolds and foliation theory: Geometirc study of hyperbolic 3-manifold: Differential structure of 4-manifolds and symplectic structures: Conformal field theory: Homotopy theory: Invariants of knots and links: General topology especially those concerned with wild spaces.In Japan, topology is developing constantly by the efforts of many researchers, and it gained worldwide recognition.Grant in aid by the Japan Society for the Promotion of Science is indispensable in this development. We express our hearty gratitude to the JSPS.

人们认识到拓扑学与其他数学领域（包括微分几何、代数、分析和数学物理）的关系，推动了拓扑学的最新进展。这使得调查方法更加复杂，研究视角更加广阔。这个研究项目的目的是使各个研究人员的合作更加容易和及时，使该领域更加活跃。我们成功地维护了拓扑学家的网络，适时地组织了各种专题讨论会和会议，进行了研究人员的交流，邀请了各种知名的国外研究人员，在国外举办了多次座谈会，为拓扑学的发展做出了重要的贡献。具体地说，我们的研究项目发展了以下拓扑领域的研究：代数和可微映射的奇异性理论；流形和简单复上的群作用；映射类群在表面的Teichmuller空间上的作用；复解析映射的动力系统理论；流形和叶理理论上向量场的动力学研究；双曲3-流形的几何研究；四流形与辛结构的微分结构；共形场理论；同伦理论；结点与连杆的不变量；一般拓扑，特别是与野空间有关的拓扑。在日本，拓扑学在许多研究者的努力下不断发展，并得到了世界范围的认可。在这一发展中，日本科学促进会的资助是不可或缺的。我们衷心感谢日本科学院。

项目成果

"Spacelike parallels and Legendrian singularities" with referee

与裁判的“类空间平行和传奇奇点”

• 发表时间: 2007
• 期刊: Journal of Geometry and Physics with referee Vol. 57
• 作者: Shuichi;Izumiya;Masatomo;Takahashi
• 通讯作者: Takahashi

Group generated by half transvections

半横断面生成的群

• 发表时间: 2005
• 期刊: Kodai Math.J. 28
• 作者: Tsuboi;Takashi
• 通讯作者: Takashi

Generic smooth maps with sphere fibers

具有球体纤维的通用平滑贴图

• 发表时间: 2005
• 期刊: J. Math. Soc. Japan 57・3
• 作者: Saeki;Osamu et al.
• 通讯作者: Osamu et al.

Parameter rigid flows on 3-manifolds

3 流形上的参数刚性流

• 发表时间: 2007
• 作者: Izumiya;Shuichi et al.;Shigenori Matsumoto
• 通讯作者: Shigenori Matsumoto

Spacelike parallels and Legendrian singularities

类空间平行线和传奇奇点

• 发表时间: 2007
• 期刊: Journal of Geometry and Physics 57
• 作者: Shuichi Izumiya;Masatomo Takahashi
• 通讯作者: Masatomo Takahashi