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Thurston's virtual fibration conjecture for finite-volume hyperbolic 3-manifolds

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Let MM be a finite-volume hyperbolic 33-manifold. A compact orientable 33-manifold is fibered if it is homeomorphic to a surface bundle over S1\mathbb{S}^1.

Thurston's virtual fibration conjecture. Every finite-volume hyperbolic 33-manifold has a finite cover that is fibered.

This conjecture is also equivalent to the statement that every finite-volume hyperbolic 33-manifold is commensurable with a fibered manifold, where two manifolds are commensurable if they share a common finite cover. Its status is not resolved in the supplied source.

References

Primary source

Melissa L. Macasieb, Kathleen L. Petersen and Ronald M. van Luijk, “On Character varieties of two-bridge knot groups”, arXiv:0902.2195 (2009).

Additional references

5 papers in this index state this conjecture (2001–2009). The statement above is taken from the most recent of them; the others are arXiv:0712.3243, arXiv:0707.4522, arXiv:math/0608415, arXiv:math/0102104.

3-manifold-topologyfibered-manifoldshyperbolic-geometry
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