Abstract: 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. I will discuss a practical algorithm for finding a diagram of a knot given a triangulation of its exterior. Our method applies to links as well as knots, and allows us to recover links with hundreds of crossings. This is joint work with Nathan Dunfield and Malik Obeidin.
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