树上群作用的超有限性

Pub Date : 2024-04-19 DOI:10.1090/proc/16851

Srivatsav Kunnawalkam Elayavalli, Koichi Oyakawa, Forte Shinko, Pieter Spaas

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引用次数: 0

摘要

我们确定了作用于可数树的可数群的自然条件，这些条件意味着格罗莫夫边界上的诱导作用的轨道等价关系是伯尔超无限的。这个条件的例子包括acylindrical作用。我们还确定了上述条件的自然弱化，这意味着边界作用的度量超有限性。然后，我们将举例说明边界作用不是超有限的树上的群作用。

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Hyperfiniteness for group actions on trees

We identify natural conditions for a countable group acting on a countable tree which imply that the orbit equivalence relation of the induced action on the Gromov boundary is Borel hyperfinite. Examples of this condition include acylindrical actions. We also identify a natural weakening of the aforementioned conditions that implies measure hyperfiniteness of the boundary action. We then document examples of group actions on trees whose boundary action is not hyperfinite.

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