Rigidity and fixed-point property of finitely generated groups

有限生成群的刚性和定点性质

• 批准号: 21540062
• 负责人: IZEKI Hiroyasu
• 金额: $ 2.83万
• 依托单位: Keio University (2010-2011)Tohoku University (2009)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 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-21540062/
• 关键词: 有限生成群; 剛性; 固定点性質; 調和写像; ランダム群; 非正曲率空間

A group G is said to have rigidity, if the space accepting the action of G is very restrictive. A group G is said to have fixed-point property for a space Y, if every action of G fixes a point in Y. Recent development of mathematical research suggests that there are plenty of groups having rigidity. We proved that, in a certain model, groups have strong fixed-point property with high probability.

如果群G的作用空间是严格的，则称群G具有刚性。称群G对空间Y具有不动点性质，如果G的每个作用都使Y中的一个点不动。数学研究的最新进展表明，存在着大量的具有刚性的群体。证明了在一定的模型下，群具有高概率的强不动点性质。

项目成果

A fixed-point property of finitely generated groups and an energy of equivariant maps

有限生成群的定点性质和等变映射的能量

• 期刊: proceedings of the 1st MSJ-SI "Probabilistic Approach to Geometry" (採用決定)
• 作者: 加藤耕;豊巻敦人;室橋春光;H. Izeki
• 通讯作者: H. Izeki