In [Doc. Math. 18 (2013), 1045–1087], Agol proved the Virtual Haken and Virtual Fibering Conjectures by confirming a conjecture of Wise: Every cubulated hyperbolic group is virtually special. We extend this result to cocompactly cubulated relatively hyperbolic groups with minimal assumptions on the parabolic subgroups. Our proof proceeds by first recubulating to obtain an improper action with controlled stabilizers (a weakly relatively geometric action), and then Dehn filling to obtain many cubulated hyperbolic quotients. We apply our results to prove the Relative Cannon Conjecture for certain cubulated or partially cubulated relatively hyperbolic groups. One of our main results (Theorem A) recovers via different methods a theorem of Oregón-Reyes [Preprint, arXiv:2003.12702, 2020].

中文翻译：

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特化累积的相对双曲线群

在[文档。数学。18 (2013), 1045–1087]，Agol 通过确认 Wise 的猜想证明了虚拟 Haken 和虚拟光纤猜想：每个立方双曲群实际上都是特殊的。我们将此结果扩展到对抛物线子群的假设最小的相对双曲线群的共紧立方。我们的证明通过首先重新计算以获得具有受控稳定器的不正确作用（相对较弱的几何作用），然后进行 Dehn 填充以获得许多累积的双曲商。我们应用我们的结果来证明某些累积或部分累积的相对双曲群的相对加农猜想。我们的主要结果之一（定理 A）通过不同的方法恢复了俄勒冈-雷耶斯定理 [Preprint, arXiv:2003.12702, 2020]。