ArticleProceedings. Mathematical, physical, and engineering sciences2020
Knot polynomials of open and closed curves.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 11 papers.
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Who cites it
11 citing papers in PubMed.
- Topological Entanglement in Intrinsically Disordered Proteins: Sequence, Structural, and Functional Determinants.The journal of physical chemistry. B · 2026Article
- Topological Entanglement in Intrinsically Disordered Proteins: Sequence, Structural, and Functional Determinants.bioRxiv : the preprint server for biology · 2026Article
- Topological data analysis and topological deep learning beyond persistent homology: a review.Artificial intelligence review · 2026Article
- Entanglement transition in random rod packings.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Multi-scale Jones polynomial and persistent Jones polynomial for knot data analysis.AIMS mathematics · 2025Article
- Knot data analysis using multiscale Gauss link integral.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Knotted artifacts in predicted 3D RNA structures.PLoS computational biology · 2024Article
- Geometric Predictors of Knotted and Linked Arcs.ACS polymers Au · 2022Article
- Article
- The protein folding rate and the geometry and topology of the native state.Scientific reports · 2022Article
- Morphological Entanglement in Living Systems.Physical review. XArticle
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2 authors.
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Abstract
In this manuscript, we introduce a method to measure entanglement of curves in 3-space that extends the notion of knot and link polynomials to open curves. We define the bracket polynomial of curves in 3-space and show that it has real coefficients and is a continuous function of the curve coordinates. This is used to define the Jones polynomial in a way that it is applicable to both open and closed curves in 3-space. For open curves, the Jones polynomial has real coefficients and it is a continuous function of the curve coordinates and as the endpoints of the curve tend to coincide, the Jones polynomial of the open curve tends to that of the resulting knot. For closed curves, it is a topological invariant, as the classical Jones polynomial. We show how these measures attain a simpler expression for polygonal curves and provide a finite form for their computation in the case of polygonal curves of 3 and 4 edges.
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