Virtually Haken conjecture

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In mathematics, the virtually Haken conjecture states that every compact, orientable, irreducible 3-manifold with infinite fundamental group is virtually Haken, i.e. finitely covered by a Haken manifold.

Assuming the geometrization conjecture, the conjecture is only open for hyperbolic 3-manifolds.

The conjecture is usually attributed to Friedhelm Waldhausen, although he did not formally state it.

[edit] See also

• virtually fibered conjecture
• virtually positive Betti number conjecture

[edit] References

• Nathan Dunfield and William Thurston, The virtual Haken conjecture: experiments and examples. Geom. Topol. 7 (2003), 399--441