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STUDY ON INFINITE TRANSFORMATION GROUPS ON MANIFOLDS

流形上无限变换群的研究

基本信息

批准号：
07454013
负责人：
TSUBOI Takashi
金额：
$ 3.52万
依托单位：
THE UNIVERSITY OF TOKYO
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07454013/
关键词：
finitely presented groups diffeomorphism groups limit sets dynamical systems infinite transformation groups manifolds the Calabi invariant 保測変換

项目摘要

1. We studied the condition for a group to be finitcly gencrated and finitely presented. We gave a proof for the case where the group acts on a simply connceted space such that the quotient space is a finite simplex and the isotropy groups are finitely gencrated and finitely presented. We also gathered a lot of knowledge on the finitely generated and finitely prescnted groups.2. The study of the classifying space for the group of diffeomorphisms extends to the study of the classifying spaces for the groups of homeomorphisms of the limit sets or the end sets. We obtained several results on the topology of them. In particular, we showed that the classifying space of the group of homeomorphisms of the Menger compact space is acyclic. We presented this result in Japan and on abroad in 1995.3. We studied discrete subgroups of Lie groups. We looked at the limit set for conformal transformation groups. We constructed several examples of discrete conformal transformation groups. It will be interesting to investigate the relationship with the number theory.4. We analyzed the measure preserving transformations from the dynamical system viewpoint. We studied the Calabi invariant and the differentiability of the dynamical system. In 1996, we found a relationship between the Calabi invariant of the group of arca preserving diffeomorphisms of the disk and the Euler class of the group of diffeomorphisms of the cirele. This should be important in the future investigation. We constructed interesting examples of mcasure prescrving transformations. We continuc to analyze them.5. We asked prof. Hacfliger of the University of Geneva to review our investigation. We got a high mark on our investigation and tion as well as valuable suggestions.

1.我们研究了群有限生成和有限呈现的条件。我们给出了群作用于简单关联空间的情况的证明，使得商空间是有限单纯形，并且各向同性群是有限生成和有限呈现的。我们还收集了大量关于有限生成群和有限呈现群的知识。2．微分同胚群的分类空间的研究延伸到极限集或端集的同胚群的分类空间的研究。我们获得了关于它们的拓扑的一些结果。特别是，我们证明了门格尔紧空间同胚群的分类空间是非循环的。我们于1995.3在日本和国外介绍了这一结果。我们研究了李群的离散子群。我们研究了共形变换群的极限设置。我们构造了几个离散保角变换群的例子。研究它与数论的关系将会很有趣。4．我们从动力系统的角度分析了测度保持变换。我们研究了动力系统的卡拉比不变量和可微性。 1996年，我们发现了圆盘微分同胚群的卡拉比不变量和圆盘微分同胚群的欧拉类之间的关系。这在以后的调查中应该很重要。我们构建了 mcasure 保护转换的有趣示例。我们继续分析它们。5．我们问教授。日内瓦大学的 Hacfliger 审查了我们的调查。我们的调查和分析得到了高度评价，并提出了宝贵的建议。