COMPREHENSIVE STUDY OF TOPOLOGY

拓扑学的综合研究

• 批准号: 08304006
• 负责人: MORITA Shigeyuki
• 金额: $ 12.61万
• 依托单位: 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: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08304006/
• 关键词: 3 manifolds; homotopy theory; transformation theory; gauge theory; singularity theory; dynamical systems; foliation; moduli space

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.

我们已经组织了一些研讨会上的各种重要议题的拓扑结构，并在每一个我们做了讲座和讨论。更具体地说，我们的主要结果如下。(i)我们在三维和四维流形的拓扑学和几何学方面取得了很大的发展。特别地，我们得到了一个关于三维流形的拓扑不变量的世界性结果。我们在双曲几何和纽结理论的研究中也取得了很大的成就。(ii)对于同伦理论和变换理论，我们在前人的基础上，得到了与代数K-理论、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新结果。(iv)我们增加了新的发展，奇异性理论，动力系统和理论的叶理。(v)我们在规范理论和数学物理方面对辛几何有了更深的理解。(vi)我们已经开始了一个新的项目，追求拓扑学和计算机科学之间的理论接口。

项目成果

KAWAUCHI, Akio: "Mutative hyperbolic homology 3-spheres with the same floer homology" Geometry dedicata. 61. 205-217 (1996)

KAWAUCHI, Akio：“具有相同弗洛尔同源性的突变双曲同源 3 球体”几何奉献。

MORITA,Shigeyuki: "A linear representation of the mapping class group of orientable surfaces and characteristic classes of surface bundles" Proceedings of Taniguchi Symposium. 159-186 (1996)

MORITA，Shigeyuki：“可定向曲面的映射类群和曲面束的特征类的线性表示”谷口研讨会论文集。

MATUMOTO, Takao: "Kusternik-schnierelman category and knot complement II" Topology. 34. 177-184 (1995)

MATUMOTO，Takao：“Kusternik-schnierelman 范畴和结补 II”拓扑。

Sadayosi KOJIMA: "Immersed geodesic surfaces in hyperbolic 3 manifolds" Complex Variables Theory and Applications. 29. 45-58 (1996)

Sadayosi KOJIMA：“双曲 3 流形中的浸没测地线表面”复变量理论和应用。

KAWAUCHI,Akio: "Mutative hyperbolic homology 3-manifolds with the same Floer homology" Geometry Dedicata. 61. 205-217 (1996)

KAWAUCHI，Akio：“具有相同 Floer 同源性的突变双曲同源 3-流形”Geometry Dedicata。