Computing a Link Diagram from Its Exterior

@inproceedings{Dunfield2021ComputingAL,
  title={Computing a Link Diagram from Its Exterior},
  author={Nathan M. Dunfield and Malik Obeidin and Cameron Gates Rudd},
  booktitle={International Symposium on Computational Geometry},
  year={2021}
}
A knot is a circle piecewise-linearly embedded into the 3-sphere. The topology of a knot is intimately related to that of its exterior, which is the complement of an open regular neighborhood of the knot. Knots are typically encoded by planar diagrams, whereas their exteriors, which are compact 3-manifolds with torus boundary, are encoded by triangulations. Here, we give the first practical algorithm for finding a diagram of a knot given a triangulation of its exterior. Our method applies to… 

All Known Principal Congruence Links

This report lists the link diagrams in S^3 for all principal congruence link complements for which such a link diagram is known. Several unpublished link diagrams are included. Related to this, we

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