Virtually Haken surgery conjecture for hyperbolic knot manifolds
A knot manifold is an irreducible, orientable, compact 3-manifold whose boundary is a single torus. It is hyperbolic if its interior admits a complete hyperbolic metric of finite volume. A slope on a torus is a non-trivial isotopy class of simple closed curves, and denotes Dehn filling a 3-manifold along a slope on its torus boundary. A knot manifold has Property VH if is virtually Haken for all but finitely many slopes on . Virtually Haken surgery conjecture. Let be a hyperbolic knot manifold. Then has Property VH. This is identified as an important special case of Waldhausen's conjecture; the source does not state whether it has been resolved.
References
Primary source
Joseph D. Masters, “Virtually Haken surgeries on once-punctured torus bundles”, arXiv:math/0506443 (2006).
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