Agol, Ian

The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning).

Doc. Math., J. DMV 18, 1045-1087 (2013)


Summary: 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 citeAGM08.

Mathematics Subject Classification

57M, 20F67


hyperbolic, group, haken