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Möbius-invariant knot energies. (English) Zbl 0945.57006

Stasiak, A. (ed.) et al., Ideal knots. Singapore: World Scientific. Ser. Knots Everything. 19, 315-352 (1998).
Summary: There has been recent interest in knot energies among mathematicians and natural scientists. When discretized, such energies can lead to effective algorithms for recognizing when two curves represent the same knot. These energies may also help model physical systems, such as long protein chains or DNA knots, subject to van der Waals interactions. Knot energies often are normalized to be scale-invariant; some important energies are also invariant under Möbius transformations of space. We describe computer experiments with such Möbius-invariant knot energies. We also discuss ways of extending these to energies for higher-dimensional submanifolds. The Appendix gives a table of computed Möbius-energy-minimizing knots and links through eight crossings. (This article is an updated version of our report in ‘Geometric topology’ [AMS/IP Stud. Adv. Math. 2 (pt. 1), 570-604 (1997; Zbl 0888.57012)].
For the entire collection see [Zbl 0915.00018].

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
57N35 Embeddings and immersions in topological manifolds

Citations:

Zbl 0888.57012
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