Synthetic Studies ofTopology

拓扑学的最新进展是由于人们认识到它与微分几何、代数、分析和数学物理等其他数学领域的关系。这使得调查方法更加复杂，并为研究提供了更广阔的视角。本研究项目的目的是方便和及时地进行各种研究人员的合作，使该领域更加活跃。我们成功地维护了拓扑学家的网络，及时地组织了各种研讨会和会议，进行了研究人员的交流，邀请了各种知名的外国研究人员，在国外举行了许多学术讨论会，具体地说，我们的研究项目发展了以下拓扑学领域的研究：代数和可微映射的奇点理论：流形和单纯复形上的群作用：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：流形上向量场的动力学研究和叶理理论：双曲3流形的几何研究：4流形的微分结构和辛结构：共形场论：同伦理论：纽结和链环的不变量：一般拓扑学，特别是那些与野生空间有关的拓扑学。在日本，拓扑学在许多研究人员的努力下不断发展，并获得了世界范围的认可。日本科学促进会的资助是这一发展不可或缺的。我们对JSPS表示衷心的感谢。

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.