Geodesic
The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning).
Documenta mathematica, Tome 18 (2013), pp. 1045-1087

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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 citeAGM08.
DOI : 10.4171/dm/421
Classification : 20F67
Mots-clés : hyperbolic, group, haken 
Ian Agol. The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning).. Documenta mathematica, Tome 18 (2013), pp. 1045-1087. doi: 10.4171/dm/421
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     title = {The virtual {Haken} conjecture (with an appendix by {Ian} {Agol,} {Daniel} {Groves} and {Jason} {Manning).}},
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