Geometry and topology of 3-manifolds II

三流形的几何和拓扑 II

基本信息

批准号：
15204004
负责人：
KOJIMA Sadayoshi
金额：
$ 11.32万
依托单位：
TOKYO INSTITUTE OF TECHNOLOGY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

项目摘要

The purpose of this research project is to see the interaction of various geometric structures on 3-manifolds, to find principal idea behind them such as laws in physics and to promote the study of 3-manifolds interacting geometry and topology interdisciplinary. The current project based on the primary one that terminated on March 2003 was set up for 4 years and we have spent 3 years so far. Then we have decided to pre-renew the project by shifting the stress more on invariants because it seems to be necessary to do so in the light of recent progress on the current working subject. Fortunately, the new project was awarded as a continuing one and thus we here report our activity of the last 3 years.In the last 3 years, we, the member of research group and collaborators, have promoted the project by doing research communication, organizing meetings and publishing research reports. As conclusion, we, the member of research group, have obtained a plenty of significant progress and simultaneously contributed the progress of this field. The research results were presented in the academic meetings including international ones. The details including one's by collaborators can be found in the attached report. In summary, according to the purpose of the project, we have darified what is needed for geometric methods to study topology of 3-manioflds more and more.Looking at last 3 years, we must notice historical progress such as the solution of the ending lamination conjecture by Minsky-Brock-Canary the solution of Marden's conjecture by Agol and Calegari-Gabai and the approach to the geometrization by Hamilton and Perelman, which at least includes the solution of Poincare conjecture. Based on these, we set up the post geometrization by renewing our project with entitling "The geometry and invariants of 3-manifolds".

该研究项目的目的是观察3流形上各种几何结构的相互作用，找到其背后的主要思想，例如物理定律，并促进3流形相互作用几何和拓扑跨学科的研究。目前的项目是在2003年3月结束的第一期的基础上进行的，历时4年，目前我们已经用了3年了。然后，我们决定通过将重点更多地转移到不变量上来预先更新该项目，因为鉴于当前工作主题的最新进展，似乎有必要这样做。幸运的是，这个新项目被授予了一个持续项目，因此我们在这里报告我们过去三年的活动。在过去的三年里，我们作为研究组的成员和合作者，通过进行研究交流、组织会议并发表研究报告。综上所述，我们作为研究组的成员，已经取得了很多重大进展，同时也为该领域的进步做出了贡献。研究成果在国际学术会议上发表。包括合作者的详细信息可以在随附的报告中找到。综上所述，根据项目的目的，我们越来越明确了用几何方法来研究三流形拓扑所需要的东西。回顾过去的三年，我们必须注意到历史的进展，例如最终层压的解决Minsky-Brock-Canary 的猜想、Agol 和 Calegari-Gabai 的 Marden 猜想的解以及 Hamilton 和 Perelman 的几何化方法，其中至少包括以下解庞加莱猜想。基于这些，我们通过更新我们的项目来建立后几何化，标题为“3-流形的几何和不变量”。