Virtually Haken Conjecture
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High Quality Content by WIKIPEDIA articles! 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.

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High Quality Content by WIKIPEDIA articles! 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.