Geometry and Topology of 3-Manifolds

三流形的几何和拓扑

基本信息

批准号：
12440015
负责人：
KOJIMA Sadayoshi
金额：
$ 7.17万
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 (B)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

项目摘要

This project was aimed to develop the interdisciplinary study of 3-manifolds which interacts geometry and topology based on the connection between several structures related mainly with hyperbolic geometry. We have in fact promoted our project in conjunction with the activity of the Topology Research Congress.We made certain significant progresses during these three research years which turned out to be rather surprising than what we had expected. The study of myself together with Mizushima and Tan on circle packings on surfaces with projective structures has clarified an expected global structure of their moduli space in the light of the deformation theory of hyperbolic 3-manifolds. The study of Yoshida on SU(2) conformal field theory has established successfully an explicit description of a basis of conformal blocks, and has approached to the fundamental connection between the geometry and topology of 3-manifolds suggested for instance by the volume con-jecture. Also, the global diagram in the 3-manifold topological invariant world suggested by Ohtsuki was completed quite recently in the most universal way by Habiro and Le. In addition, there have been down-to-earth progresses by other collaborators such as Morita's study on the mapping class group of surfaces, Matsumoto's on foliations, Sakuma's on knots and geometric structures, Soma's on bounded cohomology,In conclusion, our research has clarified the object on which we should now focus for finding the mathematical principle behind the interaction between many structures observed in the 3-manifold theory. Note in addition, the theme was fortunately funded for further study as the part II.

该项目的目的是基于几种与双曲线几何相关的几种结构之间的联系，开发3个manifolds的跨学科研究，该研究与几何和拓扑相互作用。实际上，我们与拓扑研究大会的活动一起促进了我们的项目。在这三个研究年份中，我们取得了一定的重大进展，事实证明，这比我们预期的要令人惊讶。根据双曲线3个manifolds的变形理论，与我的圆形包装上的Mizushima和Tan一起研究，阐明了其模量空间的预期全球结构。吉田对SU的研究（2）保形场理论成功地建立了对共形块基础的明确描述，并已探讨了通过体积概念提出的3个序列的几何形状和拓扑之间的基本联系。此外，Ohtsuki建议的3个式拓扑不变世界中的全球图是由Habiro和Le以最普遍的方式完成的。此外，其他合作者（例如，莫里塔（Morita）对映射阶层的绘制阶级，松本（Matsumoto），关于叶子的叶子，萨库马（Sakuma）的结论和几何结构的研究，索马（Soma）的研究，关于有限共有界共同体的研究，我们的研究应该阐明了几个构建的对象，我们应该阐明几个构造的构造 - 在界定的对象中，索马（Soma oon on Some）进行了三个构造，索马（Soma oon on Soma）的构图和几何结构上已经存在脚踏实地的进步。请注意，此外，该主题幸运地作为第二部分进行了进一步研究。