Inspired by the rather lengthy discussion on the low-dimensional topology blogthe low-dimensional topology blog, there's a rather basic question for 3-manifold algorithmics that is still unsolved, as far as I know.
- If a 3-manifold $M$ admits a complete hyperbolic structure of finite volume, does it admit an ideal triangulation? i.e. the kind of triangulation where the software SnapPy could find its hyperbolic structure.
It would be nice to either understand the hyperbolic manifolds that SnapPy (in its current state) can not deal with. Or if such manifolds do not exist, have a sense for how complicated the triangulation needs to be in order to find the hyperbolic structure.
