映射类群的独角路与超有限性
Unicorn paths and hyperfiniteness for the mapping class group
摘要：
设S是有限型的可定向曲面。利用Pho-On的无限独角路，证明了S的映射类群在弧图和曲线图的Gromov边界上的作用所诱导的轨道等价关系的超有限性.在曲线图的情况下，这加强了Hamenstädt和Kida的结果，即这种作用是普遍适用的，S的映射类群是精确的。
英文摘要：
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.
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