Geometric study on infinite simple groups

无限简单群的几何研究

• 批准号: 21654009
• 负责人: TSUBOI Takashi
• 金额: $ 2.11万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21654009/
• 关键词: 無限単純群; 微分同相群; 完全群; 幾何学的群論; 幾何学; トポロジー; 代数学

We studied infinite simple groups as geometric objects where they have verious quasimorphisms and the distance function d on the set of unions of a conjugate class and its inverse. We determined the quasi isometry type with respect to the distance d of the infinite alternative group A_infty. We showed and published the result that the identity component of the group of real analytic diffeomorphisms of a manifold with good circle actions is perfect. We showed and published the result that the identity component of the group of diffeomorphisms of a closed connected manifold of dimensions not eaual to 2 and 4 is uniformly perfect and uniformly simple. We also studied the homeomorphism groups of commutator width one.

研究了具有各种拟同构的无限单群的几何对象，以及它们在共轭类及其逆的并集上的距离函数d。我们确定了无限交错群A_infty关于距离d的拟等距型。我们证明并发表了一个结果，即具有好的圈作用的流形的真实的解析同态群的单位分支是完备的。我们证明并发表了一个结果：维数不等于2和4的闭连通流形的复同态群的单位分支是一致完备的和一致单的.我们还研究了交换子宽度为1的同胚群。

项目成果

Classifying spaces for groupoid structures, Foliations, Geometry, and Topology : Paul Schweitzer Festschrift

群状结构、叶状结构、几何形状和拓扑结构的分类空间：Paul Schweitzer Festschrift

• 发表时间: 2009
• 期刊: Contemporary Mathematics 498
• 作者: 大田春外;酒井政美;Takashi Tsuboi
• 通讯作者: Takashi Tsuboi

ON THE UNIFORM SIMPLICITY OF DIFFEOMORPHISM GROUPS

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

Classifying spaces for groupoid structures

群形结构的空间分类

• 发表时间: 2009
• 期刊: Contemporary Mathematics 498
• 作者: Soichiro Asami;Ken'ichi Kuga;山田耕三;Ken-ichi Sugiyama;Ken-ichi Sugiyama;Takashi Tsuboi
• 通讯作者: Takashi Tsuboi

On the group of real analytic diffeomorphisms

关于实解析微分同胚群

• 发表时间: 2009
• 期刊: Annales Scientifiques de l'Ecole Normale Superieure 49
• 作者: Takashi Inaba;Yosuke Kano;Iiusuo Nishijima;Takashi Tsuboi
• 通讯作者: Takashi Tsuboi

Diff^ω(CP^2)_0,「複素解析的ベクトル場・葉層構造とその周辺」

Diff^ω(CP^2)_0,“复杂解析矢量场/叶状结构及其周围环境”

• 发表时间: 2009
• 作者: Norio Iwase;Michihiro Sakai;Norio Iwase;Norio Iwase;Norio Iwase;Norio Iwase;Norio Iwase;Norio Iwase;Norio Iwase;Norio Iwase;Norio Iwase;Norio Iwase;Norio Iwase;岩瀬則夫;Norio Iwase;Norio Iwase;Norio Iwase;Norio Iwase;岩瀬則夫;Norio Iwase;岩瀬則夫;岩瀬則夫;Takashi Tsuboi;Takashi Tsuboi;Takashi Tsuboi;Takashi Tsuboi;Takashi Tsuboi;Takashi Tsuboi;Takashi Tsuboi;Takashi TSUBOI;Takashi Tsuboi;akashi TSUBOI;Takashi Tsuboi;坪井俊
• 通讯作者: 坪井俊