自同构系统的拓扑刚性

打开文本图片集

摘要：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。

关键词：自同构系统；广群；连续强轨道等价；共轭

中图分类号： O189.11                        文献标志码： A文章编号： １６７３－２３４０（２０24）０3－００89－０6

Abstract： This paper studies the automorphism actions of countable discrete groups on the étale 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.

Key words： automorphism system; groupoid; continuous strong orbit equivalence; conjugacy

算子代数与遍历理论之间的相互作用始于Murray和von Neumann关于群von Neumann代数的构造[1]。（剩余10141字）