COMPREHENSIVE STUDY OF TOPOLOGY

我们组织了许多关于拓扑学中各种重要主题的研讨会，并在每个研讨会上进行了讲座和讨论。更具体地说，我们的主要成果如下。(1)我们在三维和四维流形的拓扑和几何方面有了很大的发展。特别地，我们得到了关于3流形拓扑不变量的一个世界性的结果。我们在双曲几何和结理论的研究上也取得了巨大的成功。（ii）在同伦理论和变换理论方面，我们复习了以往的观点，得到了与代数k论、数论以及代数几何有密切联系的新结果。（iii）我们获得了关于黎曼曲面模空间拓扑的基本新结果。（四）增加了奇点理论、动力系统和叶理理论的新进展。(5)我们对辛几何与规范理论和数学物理的联系有了更深的了解。我们已经开始了一个新的项目来研究拓扑学和计算机科学之间的理论联系。

We have organized number of workshops on various important topics in topology and in each of them we made lectures and discussions. More concretely, our principal results are as follows.(i) We have made a great development in topology and geometry of 3 and 4 dimensional manifolds. In particular, we obtained a worldwide result concerning topological invariants of 3 manifolds. We also have great success in the study of hyperbolic geometry and knot theory.(ii) As to homotopy theory and transformation thoery, we went over former points of view to obtain new results which have close connection with algebraic K-theory, number theory as well as algebraic geometry.(iii) We obtained essentially new results concerning the topology of the moduli space of Riemann surfaces.(iv) We added new developments in singularity theory, dynamical systems and the theory of foliations.(v) We have achieved deeper understanding of the symplectic geomtry in connection with the gauge theory and mathematical physics.(vi) We have begun a new project to persue theoretical interface between topology and computer science.