Virtually Haken Conjecture

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Bol Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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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