Specializing cubulated relatively hyperbolic groups. Issue 2 (27th April 2022)

• Record Type: Journal Article
• Authors: Groves, Daniel; Manning, Jason Fox
• Is Part Of: Journal of topology. Volume 15:Issue 2(2022)
• Page Start: 398
• Page End: 442
• Publication Date: 2022-04-27
• Subjects: Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12226
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: 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].