Virtually Haken conjecture
- Virtually Haken conjecture
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.
ee also
* virtually fibered conjecture
* virtually positive Betti number conjecture
References
* Nathan Dunfield and William Thurston, " [http://dx.doi.org/10.2140/gt.2003.7.399 The virtual Haken conjecture: experiments and examples] ", Geom. Topol. 7 (2003) 399–441
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