Triangulations of Hyperbolic 3-Manifolds Admitting Strict Angle Structures
it is conjectured that every hyperbolic 3-manifold with torus boundary components has a decomposition into positive volume ideal hyperbolic tetrahedra (a "geometric" triangulation). Under a mild homology assumption on the manifold, we construct topological ideal triangulations which admit a "strict angle structure", which is a necessary condition for a triangulation to be geometric. In particular, every knot or link complement in S^3 that is hyperbolic has such a triangulation. This is joint work with Craig D. Hodgson and J. Hyam Rubinstein.