Convex hulls and isometries of cusped hyperbolic 3-manifolds

Jeffrey R. Weeks
1993 Topology and its Applications  
Weeks, J.R., Convex hulls and isometries of cusped hyperbolic 3-manifolds, Topology and its Applications 52 (1993) 127-149. An algorithm for computing canonical triangulations of cusped hyperbolic 3-manifolds provides an efficient way to determine whether two such manifolds are isometric. The canonical triangulation is defined via a convex hull construction in Minkowski space. The algorithm accepts as input an arbitrary triangulation (which typically corresponds to a nonconvex solid in
more » ... space) and locally modifies it until it arrives at the canonical triangulation (which corresponds to the convex hull). The practicality of the algorithm rests on a surprisingly simple theorem which detects where the local modifications must be made. The algorithm has found many applications; for example, it quickly determines whether two hyperbolic knots are equivalent.
doi:10.1016/0166-8641(93)90032-9 fatcat:kgx7gsjkhfga7g4z7cjjrfo52a