Diffeomorphism group of the circle and discontinuous groups of theuniversal Teichmuller curve

圆的微分同胚群与通用Teichmuller曲线的不连续群

• 批准号: 22740034
• 负责人: MATSUDA Yoshifumi
• 金额: $ 2.25万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22740034/
• 关键词: 円周; 微分同相群; フックス群; 回転数; 収束群作用; 相対的双曲群; C*群環; Cannon-Thurston写像; 双曲群; 普遍タイヒミュラー曲線; C*循環; Vietoris位相

We studied a boundary of the smooth universal Teichmuller curve and the action of subgroups of diffeomorphism group of the circle on this boundary. Among actions of free product of two finite groups on the circle, we characterized Fuchsian actions in terms of rotation number.We obtained a result about simplicity of the reduced group C*-algebra of a group admitting convergence actions. We gave a necessary and sufficient condition for two geometrically finite convergence actions to admit an equivariant continuous map and applied it to construct examples of convergence actions.

我们研究了光滑的通用Teichmuller曲线的边界，以及该边界上圆圈差异基团的亚组的作用。在圆圈上两个有限组的自由产品的动作中，我们在旋转数方面表征了紫红色的作用。我们获得了一个降低的组C*-Algebra组的结果，该组允许收敛动作。我们为两种几何有限的收敛动作提供了必要的条件，以接收一个模棱两可的连续图，并将其应用于构造收敛作用的示例。

项目成果

On the isometry group of the universal Teichmuller curve

论通用Teichmuller曲线的等距群

• 发表时间: 2010
• 作者: 後藤四朗;大関一秀;笹木集夢;Shiro Goto and Kazuho Ozeki;笹木集夢;Hiroshige Kajiura;笹木集夢;Hiroshige Kajiura;Hiroshige Kajiura;Atsumu Sasaki;Atsumu Sasaki;Atsumu Sasaki;笹木集夢;笹木集夢;Y. Matsuda;Masaharu Ishikawa;Yoshifumi Matsuda;Y. Matsuda;笹木集夢;Masaharu Ishikawa;西納武男;Masaharu Ishikawa;笹木集夢;Masaharu Ishikawa;Yoshifumi MASTSUDA
• 通讯作者: Yoshifumi MASTSUDA

Blowing up and down compacta with geometrically finite convergence actions of a group

• 发表时间: 2012-01
• 期刊: arXiv: Group Theory
• 作者: Yoshifumi Matsuda;Shin-ichi Oguni;S. Yamagata

The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups

群上的普遍相对双曲结构和子群的相对拟凸性

• 发表时间: 2011
• 作者: 後藤四朗;大関一秀;笹木集夢;Shiro Goto and Kazuho Ozeki;笹木集夢;Hiroshige Kajiura;笹木集夢;Hiroshige Kajiura;Hiroshige Kajiura;Atsumu Sasaki;Atsumu Sasaki;Atsumu Sasaki;笹木集夢;笹木集夢;Y. Matsuda;Masaharu Ishikawa;Yoshifumi Matsuda;Y. Matsuda
• 通讯作者: Y. Matsuda