Thurston's virtual fibration conjecture for finite-volume hyperbolic 3-manifolds
Thurston's virtual fibration conjecture for finite-volume hyperbolic 3-manifolds
Let be a finite-volume hyperbolic -manifold. A compact orientable -manifold is fibered if it is homeomorphic to a surface bundle over .
Thurston's virtual fibration conjecture. Every finite-volume hyperbolic -manifold has a finite cover that is fibered.
This conjecture is also equivalent to the statement that every finite-volume hyperbolic -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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