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

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

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 l...

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Hauptverfasser: Arai, Masafumi, Taniyama, Kouki
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Mathematics - Geometric Topology
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description 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.
doi_str_mv 10.48550/arxiv.2002.09709
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title Knot diagrams on a punctured sphere as a model of string figures
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