Knot diagrams on a punctured sphere as a model of string figures

Masafumi Arai; Kouki Taniyama

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arXiv · 2002.09709

Knot diagrams on a punctured sphere as a model of string figures

Masafumi Arai·Kouki Taniyama

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Abstract

A string figure is topologically a trivial knot lying on an imaginary plane orthogonal to the fingers with some crossings. The fingers prevent cancellation of these crossings. As a mathematical model of string figure we consider a knot diagram on the $xy$-plane in $xyz$-space missing some straight lines parallel to the $z$-axis. These straight lines correspond to fingers. We study minimal number of crossings of these knot diagrams under Reidemeister moves missing these lines.

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Masafumi Arai, Kouki Taniyama. 2020-02-22. Knot diagrams on a punctured sphere as a model of string figures. https://arxiv.org/abs/2002.09709

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