Let S be an orientable surface of finite type. Using Pho-on’s infinite unicorn paths, we prove the hyperfiniteness of orbit equivalence relations induced by the actions of the mapping class group of S on the Gromov boundaries of the arc graph and the curve graph of S. In the curve graph case, this strengthens the results of Hamenstädt and Kida that this action is universally amenable and that the mapping class group of S is exact.

中文翻译：

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映射类组的独角兽路径和超有限性

让小号是有限类型的可定向曲面。利用 Pho-on 的无限独角兽路径，我们证明了由小号关于弧图和曲线图的 Gromov 边界小号. 在曲线图的情况下，这加强了 Hamenstädt 和 Kida 的结果，即这个动作是普遍适用的，并且映射类组小号是准确的。