Groups of diffeomorphisms of manifolds

流形微分同胚群

• 批准号: 20244003
• 负责人: TSUBOI Takashi
• 金额: $ 28.2万
• 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 (A)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-20244003/
• 关键词: 幾何学; トポロジー; 多様体; 微分同相群; 分類空間; 力学系; 離散部分群; 位相亜群; 葉層構造; 微分トポロジー

We studied the group of diffeomorphisms which is the automorphism group of the manifold structure. The principal investigator obtained results on the perfectness of the identity component of the group of real-analytic diffeomorphisms,the uniform perfectness and the uniform simplicity of the identity component of the group of smooth diffeomorphisms, and published them. The co-investigators obtained results on the mapping class group of surfaces, on the transversely holomorphic foliations, on connecting lemma in the theory of dynamical systems, and published them. Each year we organized meeting on the diffeomorphism groups for the collaboration and exchange the research ideas.

本文研究了流形结构的自同构群--自同构群。主要研究人员获得的结果完善的身份组成部分的一组真正的分析cruomorphisms，一致完善性和一致简单性的身份组成部分的一组顺利cruomorphisms，并公布他们。共同调查人员获得的结果映射类组的表面，在横向全纯叶理，连接引理理论的动力系统，并出版。每年我们都组织同晶组的会议进行合作和交流研究思想。

项目成果

Integral Riemann-Roch formulae for cyclic subgroups of mapping class groups

映射类群循环子群的积分Riemann-Roch公式

• 发表时间: 2008
• 期刊: Math. Proc. Cambridge Phil. Soc. 144
• 作者: T. Akita;and Nariya Kawazumi
• 通讯作者: and Nariya Kawazumi

Godbillon-Vey class of transversely holomorphic foliations.

Godbillon-Vey 类横向全纯叶状结构。

• 发表时间: 2010
• 期刊: MSJ memoirs 24
• 作者: Toshiakira Fujii;Brian Doing;Susie Groves;Takashi Shioya;Wataru Nakazawa;C. Amiot;金子文夫;姉崎洋一・宋美蘭・石山貴士;堀潔;R.Goto;藤田弘夫・橋本和孝・吉原直樹;Taro Asuke
• 通讯作者: Taro Asuke

ON THE UNIFORM SIMPLICITY OF DIFFEOMORPHISM GROUPS

• DOI: 10.1142/9789814261173_0004
• 发表时间: 2009-04
• 作者: T. Tsuboi

Codimension one minimal foliations and the fundamental groups of leaves

余维一最小叶状结构和基本叶群

• 发表时间: 2008
• 期刊: Annale de l'Institut Fourier 58
• 作者: Tomoo Yokoyama;Takashi Tsuboi
• 通讯作者: Takashi Tsuboi

On the Turaev cobracket on the Lie algebra of symplectic derivations

辛导数李代数上的 Turaev cobracket

• 发表时间: 2011
• 作者: 村田 伸;津田 彰;Nariya Kawazumi
• 通讯作者: Nariya Kawazumi