COMPREHENSIVE STUDY OF TOPOLOGY

点击翻译按钮获取中文摘要

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.