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

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.

Sources & referencesView supporting material

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.

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