Unknotting operations of rotation type (Q1210372)

This paper is concerned with knots and links in \(S^ 3\). \textit{Y. Nakanishi} [ibid. 14, No. 1, 197-203 (1991; Zbl 0742.57007)] showed that the six replacements appearing in the Conway third identity are all unknotting operations, and determined the number of equivalence classes for the equivalence relation generated by each replacement for a \(\mu\)- component link. \textit{H. Aida} [ibid. 15, No. 1, 111-121 (1992; Zbl 0773.57003)] generalized two of these replacements to an \(n\)-gon move and showed that it is an unknotting operation. In this paper, we generalize the rest of the six replacements to moves of polygon type similarly as Aida did, and show that any \(\mu\)-component link can be deformed into a trivial knot by a finite sequence of each of these moves.