Two localized, stable versions of the Jones polynomial are introduced for analyzing local and global entanglement of open curves, with applications to protein B-factor prediction.
Parity in Knotoids
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
This paper investigates the parity concept in knotoids in $S^2$ and in $\mathbb{R}^2$ in relation with virtual knots. We show that the virtual closure map is not surjective and give specific examples of virtual knots that are not in the image. We introduce a planar version of the parity bracket polynomial for knotoids in $\mathbb{R}^2$. By using the Nikonov/Manturov theorem on minimal diagrams of virtual knots we prove a conjecture of Turaev showing that minimal diagrams of knot-type knotoids have zero height.
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2024 1verdicts
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Multiscale Jones Polynomial and Persistent Jones Polynomial for Knot Data Analysis
Two localized, stable versions of the Jones polynomial are introduced for analyzing local and global entanglement of open curves, with applications to protein B-factor prediction.