ArticleDiscrete & computational geometry2024
Computing a Link Diagram From Its Exterior.
Article in Discrete & computational geometry, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
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1 citing paper in PubMed.
- Computing a Link Diagram From Its Exterior.Discrete & computational geometry · 2024Article
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3 authors.
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Abstract
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 links as well as knots, and allows us to recover links with hundreds of crossings. We use it to find the first diagrams known for 23 principal congruence arithmetic link exteriors; the largest has over 2500 crossings. Other applications include finding pairs of knots with the same 0-surgery, which relates to questions about slice knots and the smooth 4D Poincaré conjecture.
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