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.

我们把无限单群作为几何对象来研究，其中它们具有丰富的拟态，以及共轭类及其逆的并集上的距离函数d。确定了关于无限交错群A_INFTY的距离d的拟等距类型。我们证明并发表了具有良好圆作用的流形的实解析微分同胚群的单位分支是完全的。我们证明并发表了不等于2和4的闭连通流形的微分同胚群的恒等式分支是一致完美和一致单的。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