Quasiconvexity and Dehn filling

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 a recent result 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 the results of [2, Appendix A] can be generalized to the relative setting to control the relative height of relatively quasiconvex subgroups under appropriate Dehn fillings.

33 pages, 3 figures. To appear in American Journal of Mathematics. v3: Fixed typo in Example 4.8