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.

我们研究了微分同胚群，即流形结构的自同构群。主要研究者得到了实解析微分同胚群的恒等分量的完备性、光滑微分同胚群的恒等分量的一致完备性和一致简单性的结果，并发表。共同研究人员在动力系统理论中的曲面映射类群、横向全纯叶状结构、连接引理方面取得了成果，并发表了它们。每年我们都会组织微分同胚组会议以进行合作和交流研究想法。

项目成果

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

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

On Fatou-Julia decompositions of pseudosemigroups

关于伪半群的 Fatou-Julia 分解

• 发表时间: 2010
• 期刊: 数理解析研究所講究録
• 作者: Takahashi;M.;Lauwereyns;J.;Sakurai;Y. and Tsukada;M.;Taro Asuke
• 通讯作者: Taro Asuke

The Chas-Sullivan conjecture for a surface of infinite genus

无限亏格面的 Chas-Sullivan 猜想

• 发表时间: 2010
• 作者: J. Xu;J. Xiong and S. Kawashima;H.Ishi;河澄響矢
• 通讯作者: 河澄響矢