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Convex hulls and isometries of cusped hyperbolic 3-manifolds
<span title="">1993</span>
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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
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... 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.
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