论文标题
相对双曲群的边界作用的过度使用
Hyperfiniteness of boundary actions of relatively hyperbolic groups
论文作者
论文摘要
我们表明，如果$ g $是有限生成的组双曲线相对于有限的子组$ \ Mathcal {p} $的收集，则$ g $在相关的相对Cayley图的地球边界上的自然作用会引起高频等效性。作为推论，我们获得了$ g $在其Bowditch边界$ \ partial（G，\ Mathcal {p}）$上的自然作用也引起了高限度的等价关系。这加强了Ozawa为$ \ Mathcal {p} $获得的Ozawa的结果，该{P} $由Amenable子组组成，并使用了Marquis和Sabok的最新作品。
We show that if $G$ is a finitely generated group hyperbolic relative to a finite collection of subgroups $\mathcal{P}$, then the natural action of $G$ on the geodesic boundary of the associated relative Cayley graph induces a hyperfinite equivalence relation. As a corollary of this, we obtain that the natural action of $G$ on its Bowditch boundary $\partial (G,\mathcal{P})$ also induces a hyperfinite equivalence relation. This strengthens a result of Ozawa obtained for $\mathcal{P}$ consisting of amenable subgroups and uses a recent work of Marquis and Sabok.
