虚循环群作用的连续轨道等效刚性

Pub Date : 2021-06-11 DOI:10.4171/ggd/709
Yongle Jiang
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引用次数: 4

摘要

我们证明了对于无限紧Hausdorff空间上无限二面体群的任意两个连续极小(拓扑自由)作用,只有当它们共轭时,它们才是连续轨道等价的。如果我们用某些其他虚拟循环群代替无限二面体群,例如整数群与任何非阿贝尔有限简单群的直积,我们也证明了上述方法是失败的。
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On continuous orbit equivalence rigidity for virtually cyclic group actions
We prove that for any two continuous minimal (topologically free) actions of the infinite dihedral group on an infinite compact Hausdorff space, they are continuously orbit equivalent only if they are conjugate. We also show the above fails if we replace the infinite dihedral group with certain other virtually cyclic groups, e.g. the direct product of the integer group with any non-abelian finite simple group.
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