Research on several geometry from the view point of sinuglarity theory

奇点理论视角下的几种几何学研究

基本信息

批准号：
15204002
负责人：
IZUMIYA Shyuichi
金额：
$ 32.2万
依托单位：
HOKKAIDO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

项目摘要

The purposes of the reasearch project were improvements of several areas in Topology and Differential Geometry which are roots of Singularity theory, constructions of new field for the applications of Singularity theory and developments of the applications of recent results of Singularity theory to Topology and Differential Geometry. For the purpose, we made a study on the following subjects and got many resutls : The higher order contact geomety, Symplectic Topology, Dynamical system and the theory of foliations, Knot theory, Topology on discrete groups, Topological dynamics and General Topology, geometric applications of Homotopical Algebra, groups of diffeomorphisms, Topological field theory and Riemannian geometry, Four dimensional topology.I order to exchange the above researches, we organized the national conference on Topology on each year. We also organized several conferences on the above subjects. As researches on Singularity theory, we have studied Symplectic singularity theory, Global theory on singularities of smooth mappings, Fundamental group of algebraic curves and applications of singularity theory to Differential Geometry.As a concequence, we established the puropose of the project. Especially, we organized the 12th MSJ-IRI International research institute "singularity theory and its applications" on September,2003 jointly with COE program of Hokkaido University "Nonlinear mathematics via singularities". We decided the puropose of the research project as the result of the conference. In the final year, we organized the special months "Singularity theory" (September,2005-12,2005) jointly with the above COE program. We confirmed the results of the project and the future problems in the speical months.

Reasearch项目的目的是改进拓扑和差异几何学领域的几个领域，这些几何形状是奇异理论的根源，新领域在奇异理论的应用中的构建以及奇异理论在拓扑和差异几何学上的最新结果的应用的发展。出于此目的，我们对以下主题进行了研究，并获得了许多重新统治：较高的接触几何，符号拓扑，动力学系统和叶子理论，结理论，关于离散群体的拓扑，拓扑动态和一般拓扑，拓扑动态和一般拓扑，几何学的几何学，同型代数，拓扑结构，拓扑结构阶层，拓扑结构的拓扑结构，拓扑结构，拓扑结构，拓扑结构，拓扑结构，拓扑结构，拓扑结构，拓扑结构，拓扑结构，拓扑结构，拓扑结构范围。在上面的研究中，我们每年组织了全国性拓扑会议。我们还在上述主题上组织了几次会议。正如对奇异性理论的研究，我们研究了符合性的奇异性理论，关于平滑映射的奇异性的全球理论，代数曲线的基本群体以及奇异理论在差异几何学上的应用。特别是，我们于2003年9月与北海道大学的COE计划共同组织了第12届MSJ-IRI国际研究所“奇异理论及其应用”。我们决定了会议的结果研究项目的纯胶。在最后一年，我们与上述COE计划共同组织了特殊的月份“奇异理论”（2005-12,2005）。我们确认了该项目的结果和未来的问题。