The virtual Haken conjecture

Abstract

We prove that cubulated hyperbolic groups are virtually special. The proof relies on results of Haglund and Wise which also imply that they are linear groups, and quasi-convex subgroups are separable. A consequence is that closed hyperbolic 3-manifolds have finite-sheeted Haken covers, which resolves the virtual Haken question of Waldhausen and Thurston's virtual fibering question. An appendix to this paper by Agol, Groves, and Manning proves a generalization of the main result of "Residual finiteness, QCERF and fillings of hyperbolic groups".

32 pages, 2 figures; Primary article by Ian Agol with an appendix by Ian Agol, Daniel Groves, and Jason Manning; relies on work of Dani Wise and collaborators available here: http://comet.lehman.cuny.edu/behrstock/cbms/program.html