Convex hulls and isometries of cusped hyperbolic 3-manifolds

Jeffrey R. Weeks
<span title="">1993</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="" style="color: black;">Topology and its Applications</a> </i> &nbsp;
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 &raquo; ... 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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1016/0166-8641(93)90032-9</a> <a target="_blank" rel="external noopener" href="">fatcat:kgx7gsjkhfga7g4z7cjjrfo52a</a> </span>
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