In topology, an area of mathematics, the virtually Haken conjecture states that every compact, orientable, irreducible three-dimensional manifold with infinite fundamental group is virtually Haken. That is, it has a finite cover (a covering space with a finite-to-one covering map) that is 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. This problem is formally stated as Problem 3.2 in Kirby's problem list.