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The virtual Haken conjecture


Speaker: Ian Agol, UC Berkeley
Location: 2112 MSB
Start time: Tue, Apr 24 2012, 3:10PM

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. The result depends on recent work of Wise and his collaborators, and a generalization of a result of Agol, Groves, and Manning.