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.

拓扑学的最新进展是由于认识到它与其他数学领域的关系，包括微分几何、代数、分析和数学物理。这使得调查方法更加复杂，研究视野更加广阔。该研究项目的目的是使各个研究人员的合作变得容易和及时，使该领域更加活跃。我们成功地维护了拓扑学家的网络，适时组织了各种研讨会和会议，进行了研究人员的交流，邀请了各种知名的国外学者具体而言，我们的研究项目开展了以下拓扑领域的研究：代数和可微映射的奇异性理论：群作用流形和单纯复形：曲面 Teichmuller 空间上映射类群的作用：复解析映射的动力系统理论：流形上向量场的动力学研究和叶状理论：双曲 3-流形的几何研究：4 的微分结构-流形和辛结构：共形场论：同伦论：结和链接的不变量：一般拓扑，尤其是那些与野相关的拓扑在日本，拓扑学在众多研究人员的努力下不断发展，并得到了世界范围的认可。这一发展离不开日本学术振兴会的资助。我们对JSPS表示衷心的感谢。

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

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

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.

Different links with the same Links-Gould invariant

具有相同链接-古尔德不变量的不同链接

• 发表时间: 2005
• 期刊: Osaka J. Math. 42・2
• 作者: Kanenobu;Taizo et al.
• 通讯作者: Taizo et al.