Straightening cell decompositions of cusped hyperbolic 3-manifolds
Let be an oriented cusped hyperbolic 3-manifold and let be a topological ideal triangulation of . We give a characterization for to be isotopic to an ideal geodesic triangulation; moreover we give a characterization for to flatten into a partially flat triangulation. Finally we prove that straightening combinatorially equivalent topological ideal cell decompositions gives the same geodesic decomposition, up to isometry.