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The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning)
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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 [1].
Title: The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning)
Description:
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 [1].
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