Four-genus and unknotting number of positive knots and links
An oriented link is said to be positive if it is represented by a diagram which has only positive crossings. In this paper, the author proves that every positive link is strongly quasipositive in the sense of \textit{L. Rudolph} [Comment. Math. Helv. 58, 1-37 (1983; Zbl 0522.57017)], by improving Yamada's algorithm for obtaining a braid representation from a given diagram without changing the number of Seifert circles. This result, together with the result of \textit{L. Rudolph} [Bull. Am. Math. Soc., New Ser. 29, No. 1, 51-59 (1993; Zbl 0789.57004)], determines the 4-genera of positive links. As an application, it is proved that a positive knot has unknotting number one if and only if it is a twist knot.
scientific article; zbMATH DE number 1515485