A distance on the equivalence classes of spherical curves generated by deformations of type RI
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]
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′]).
- Journal of Knot Theory and Its Ramifications
Journal of Knot Theory and Its Ramifications 27 (12), 1850066-, 2018-10-25
World Scientific Publishing