abstract:

We define a new condition on relatively hyperbolic Dehn filling which allows us to control the behavior of a relatively quasiconvex subgroups which need not be full. As an application, in combination with recent work of Cooper and Futer, we provide a new proof of the virtual fibering of non-compact finite-volume hyperbolic $3$-manifolds, a result first proved by Wise. Additionally, we explain how previous results on multiplicity and height can be generalized to the relative setting to control the relative height of relatively quasiconvex subgroups under appropriate Dehn fillings.

中文翻译：

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拟凸度和Dehn填充

摘要：

我们在相对双曲的Dehn填充上定义了一个新条件，该条件使我们能够控制不需要充满的相对拟凸子组的行为。作为一个应用程序，结合Cooper和Futer的最新工作，我们提供了非紧凑有限体积双曲线$ 3 $流形的虚拟纤维化的新证明，该结果首先由Wise证明。此外，我们解释了如何将先前关于多重性和高度的结果推广到相对设置，以控制在适当的Dehn填充下相对准凸子组的相对高度。