Four-genus and unknotting number of positive knots and links
type: Item
instance of: scholarly article
title: Four-genus and unknotting number of positive knots and links
zbMATH Open document ID: 0968.57008
author: Takuji Nakamura
published in: Osaka Journal of Mathematics
publication date: 2001-09-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 1515485
zbMATH Keywords: quasipositive link
zbMATH Keywords: 4-genus
zbMATH Keywords: positive link
zbMATH Keywords: unknotting number
reviewed by: Makoto Sakuma
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1515485