Various Aspects of Topology

拓扑的各个方面

基本信息

批准号：
12304003
负责人：
TSUBOI Takashi
金额：
$ 31.17万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12304003/
关键词：
Algebraic Topology Topology Foliations Mapping Class Groups General Topology Three Dimensional Manifolds Sinqularity Theory Gauge Theory

项目摘要

Topology is the mathematics to study the position and the shape. The development of topology in the last decade was promoted by the interaction between the branches of topology as well as that between differential geometry, algebra, analysis, mathematical physics and topology. In this research, we wish to promote the development much more. We did the researches in the following fields : classifying theory of singularities of mappings and algebraic varieties, various group actions on manifolds and simplicial complexes, the action of the mapping class groups of the surfaces on their Teichmuller spaces, the dynamical study of complex analytic maps, the dynamical study of vector fields on manifolds and foliations, the classifying theory of hyperbolic 3 dimensional manifolds and hyperbolic spaces with singularities, the differentiable structures and symplectic structures on 4 dimensional manifolds, the conformal field theory and invariants of dimensional manifolds, the topology of the moduli spaces of connections of various principal bundles, the Poisson manifolds and contact manifolds, equivariant generalized (co)homology theories and homotopy theories, invariants of knots and links and their classification, general topology theory for wild spaces. These researches were done successfully with their own results. In order to promote the interaction between these researches we held "Topology Symposium" each year as well as many conferences on the above research fields. These are done as Topology Projects in the collaboration with researchers in topology in Japan. In particular, the series of the meetings "Encounter with Mathematics" were held in order to promote the interaction with researchers in other fields as well as graduate students. By these research activities, the direction of new development for the next project became clear.

拓扑是研究位置和形状的数学。在过去十年中，拓扑的发展是通过拓扑分支之间的相互作用以及差异几何，代数，分析，数学物理学和拓扑之间的相互作用来促进的。在这项研究中，我们希望更多地促进发展。我们在以下领域中进行了研究：对映射和代数品种的奇异性进行分类，对流形和简单复合物的各种群体行动，对表面的映射类群体对TEICHMULLER空间的作用，对复杂分析图的动态研究以及对载体的动态研究的动态研究，对旋转的言像的动态研究，分类的体现，既体现的态度研究，又有曲线的动态研究。具有奇异性，可区分结构和符号结构的双曲空间，在4维流形上，保形场理论和维歧管的不变性，各种主要捆绑包的模态空间的拓扑，Poisson和Poisson的歧管和接触歧管，均等（CO）的（Co）的（CO）的常规和家用（CO）的家用和家用式的家用和家族式的旋转，并构成了他们的家用和家用。分类，野生空间的一般拓扑理论。这些研究成功完成了自己的结果。为了促进这些研究之间的相互作用，我们每年举行“拓扑研讨会”以及上述研究领域的许多会议。这些是与日本拓扑研究人员合作的拓扑项目。特别是，举行了一系列“与数学相遇”的会议，以促进与其他领域的研究人员以及研究生的互动。通过这些研究活动，下一个项目的新发展方向变得清晰。