自同构系统的拓扑刚性

Topological rigidity of automorphism systems

研究了可数离散群在紧度量空间étale等价关系上的自同构作用。文章引入了自同构系统上连续强轨道等价的定义,证明了共轭的两个自同构系统一定是连续强轨道等价的,反之,在本质自由和离散群是顺从无挠的条件下,满足刚性条件的两个连续强轨道等价的自同构系统是共轭的。

This paper studies the automorphism actions of countable discrete groups on theétale equivalence relations on compact metric spaces.First,the notion of continuous strong orbit equivalence for automorphism systems is introduced and it is proved that two conjugate automorphism systems are continuously strong orbit equivalent.Conversely,under the conditions of essentially freeness and discrete groups being amenable and torsion-free,two continuously strong orbit equivalent automorphism systems satisfying the rigid condition are conjugate.