Generalized unknotting operations of polygonal type and rotational type (Q675774)

A set of local moves on knot diagrams is called a generalized unknotting operation if any knot can be transformed into a trivial knot by successive application of the moves. In the paper under review, the author introduces a certain family of local moves which act on an \(n\)-gon in a knot diagram, generalizing the local moves introduced by \textit{H. Aida} [ibid. 15, No. 1, 111-121 (1992; Zbl 0773.57003)] and \textit{Y. Ohyama} [ibid., No. 2, 357-363 (1992; Zbl 0801.57001)]. It is proved that most of the local moves in the family are unknotting operations. Moreover, the moves are classified according to the local equivalence classes introduced by \textit{Y. Nakanishi} [J. Knot Theory Ramifications 3, No. 2, 197-209 (1994; Zbl 0823.57005)]. In the appendix, the author gives a table of \(\Delta\)-unknotting numbers of the prime knots up to \(\leq 10\) crossings except for 14 knots.