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查看3个曼膜上各种几何结构的相互作用，以找到它们背后的主要思想，例如物理学法律，并促进对3个manifolds相互作用的几何形状和拓扑跨学科的研究。目前基于2003年3月终止的主要项目已建立了4年，我们已经花费了3年了。然后，我们决定通过更多地转移不变式的压力来预先续订该项目，因为根据当前工作主题的最新进展，似乎有必要这样做。幸运的是，这个新项目被授予一个持续的项目，因此我们在这里报告了过去三年的活动。在过去的3年中，我们是研究小组和合作者的成员，通过进行研究沟通，组织会议和出版研究报告来促进该项目。总结，我们研究小组的成员已经取得了很大的进步，并同时贡献了这一领域的进步。研究结果在包括国际活动的学术会议上提出。可以在随附的报告中找到包括合作者在内的详细信息。 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至少包括庞加罗猜想的解决方案。基于这些，我们通过有权“ 3- manifolds的几何图形和不变性”来续签我们的项目，从而建立了几何化。