STUDY ON THE GROUPS OF DIFFEOMORPHISMS

微分形群的研究

基本信息

批准号：
09440028
负责人：
TSUBOI Takashi
金额：
$ 5.06万
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：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

We studied the groups of diffeomorphisms of the circle and the disk. In particular, we found an important relationship between the group of diffeomorphisms of the circle and the group of the area preserving diffeomorphisms of the disk. Namely using tha fact that any diffeomorphism of the boundary circle of the disk has an extention to an area preserving diffeomorphism of the disk, we wrote down the relationship between the Euler class for the group of diffeomorphisms of the circle and the Calabi invariant for the group of the area preserving diffeomorphisms of the disk. Moreover we showed the sane result for the groups of Lipschitz homeomorphisms.We studied similar relationship between the group of diffeomorphisms of 2-sphere and that of 3-ball, between the group of diffeomorphisms of 3-sphere and that of 4-ball, or more generally, the group of diffeonorphisms of the boundary of a compact manifold and that of the manifold. We also studied the group of Lipschitz homeomorphisms and we obtained a new result on the perfectness of such groups.Relating to the contact structure on the 3-manifolds, we investigated the generalization of the notion of the projectively Anosov flows in higher dimensions. We studied the diffeomorphism classes of such objects. We look at the algebraic models in detail. We also studied Anosov flows and found a classification for regular projectively Anosov flows without compact leaves. We also studied complex vector fields and complex contact structures.We studied the characteristic classes for foliations and the SC^-*S algebra for the foliations. In particular we investigated the case where the foliation has transversely piecewise linear structure. We also looked at the finitely presented simple groups.

我们研究了圆圈和磁盘的差异群。特别是，我们发现了圆圈的差异群与保留磁盘差异的区域之间的重要关系。即使用事实，即磁盘边界圆的任何差异性具有延伸到保留磁盘的区域的区域，我们写下了圆圈的Euler类之间的关系保存磁盘差异的区域。此外，我们展示了Lipschitz同构的群体的理智结果。我们研究了2球的二型差异和3球之间的相似关系，在3杆的差异和4球或4球或4球的差异性之间更一般地，紧凑型歧管和歧管的边界的二态构成群。我们还研究了Lipschitz同构的群体，并获得了此类组的完美性的新结果。与3个模型上的接触结构汇总，我们研究了Project Anosov流的概念在更高的维度中。我们研究了此类对象的差异类别。我们详细研究代数模型。我们还研究了Anosov流量，并发现了常规的投射性Anosov流动的分类，而没有紧凑的叶子。我们还研究了复杂的矢量场和复杂的接触结构。我们研究了叶子的特征类别和叶子的sc^ - *s代数。特别是我们研究了叶面具有横向分段线性结构的情况。我们还研究了有限的简单群体。