【10/4更新】2022年4月1日からのCiNii ArticlesのCiNii Researchへの統合について

A distance on the equivalence classes of spherical curves generated by deformations of type RI

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Electronic version of an article published as [Journal of Knot Theory and Its Ramifications, Vol. 27, No. 12, 1850066 (2018)] [https://doi.org/10.1142/S0218216518500669] World Scientific Publishing Company [https://www.worldscientific.com/worldscinet/jktr]

2019.10.26に本文公開

In this paper, we introduce a distance d˜w3 on the equivalence classes of spherical curves under deformations of type RI and ambient isotopies. We obtain an inequality that estimate its lower bound (Theorem 1). In Theorem 2, we show that if for a pair of spherical curves P and P′, d˜w3([P],[P′])=1 and P and P′ satisfy a certain technical condition, then P′ is obtained from P by a single weak RIII only. In Theorem 3, we show that if P and P′ satisfy other conditions, then P′ is ambient isotopic to a spherical curve that is obtained from P by a sequence of a particular local deformations, which realizes d˜w3([P],[P′]).

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