Diffeomorphism groups --from a view point of rigidity problem

微分同胚群--从刚性问题的角度看

基本信息

批准号：
12440016
负责人：
KANAI Masahiko
金额：
$ 6.78万
依托单位：
Nagoya University
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 2003
项目状态：
已结题

项目摘要

<Kanai> He made computation of Gelfand-Fuks cohomology of diffeomorphism groups and their homogeneous spaces especially keeping in his mind possible applications of it to rigidity problems. A new perspective on infinitesimal rigidity of Anosov actions of higher-rank abelian groups that arise from semisimple Lie groups of rank greater than one has also been obtained by him.<Izeki> It is known that the domain of discontinuity of a convex-cocompact Kleinian group is compact. Conversely, he proved that a Kleinian group is convex cocompact provided the Hausdorff dimension of the limit set is less than n/2.<Izeki and Nayatani> They introduced a combinatorial notion of harmonic map of a simplicial complex into singular space of nonpositive curvature, and showed an existence theorem under an appropriate assumption. A fixed point theorem for an isometric action of a discrete group on a nonpositively curved space has been established as an application.<Kotani> She investigated, in a joint work of T.Sunada, the large deviation principle. Another achievement by her is the Lipschitz continuity of the bounds of the spectrum of some self-adjoint operator with magnetic, effect.<Tsuboi> A projective Anosov flow is said to be regular if its stable and unstable plane fields are integrated by smooth foliations. He proved that for a regular projective Anosov flow on a Seifert fibered space if the associated foliations have no compact leaf then it is a regular Anosov flow, and in consequence is quasi-Fuksian, due to a theorem of Ghys.<Fujiwara> In the joint work with Bestvina, he made a computation of the second bounded cohomology of the mapping class groups. It follows that a discrete subgroup of a Lie group can never be realized as a subgroup of the mapping class groups.

<kanai>他对差异群体及其同质空间的Gelfand-Fuks共同体进行了计算，尤其是在他的脑海中可能将其应用于僵化问题。他对高级阿贝尔群体Anosov作用的无限刚性的新观点，是由他获得的半级别的排名群。相反，他证明了一个kleinian群体是凸起的，只要限制集的Hausdorff维度小于N/2。离散组对非弯曲空间的等轴测动作的固定点定理已作为应用。她的另一个成就是Lipschitz的连续性在某些具有磁性，效果的自相配操作员的边界的连续性。他证明，对于常规的投影型Anosov在Seifert纤维纤维上流动，如果相关的叶子没有紧凑的叶子，那么它是常规的Anosov流动，因此，由于Ghys的定理是Ghys的定理。<fujiwara>。因此，谎言组的离散子组永远无法被实现为映射类组的子组。