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="https://fatcat.wiki/container/hp7o5f6pmrg57k2m46s4syavf4" 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="https://doi.org/10.1016/0166-8641(93)90032-9">doi:10.1016/0166-8641(93)90032-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kgx7gsjkhfga7g4z7cjjrfo52a">fatcat:kgx7gsjkhfga7g4z7cjjrfo52a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171005103017/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/f1c/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMTY2ODY0MTkzOTAwMzI5.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/54/45/5445aeed1e182f21200eed8521012ae2b6fcbe48.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0166-8641(93)90032-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>