The minimal number of Seifert circles equals the braid index of a link
type: Item
instance of: scholarly article
title: The minimal number of Seifert circles equals the braid index of a link
zbMATH Open document ID: 0634.57004
DOI: 10.1007/BF01389082
author: Shuji Yamada
published in: Inventiones Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143484
review text: The Seifert circles of an oriented knot diagram are the simple closed curves in the plane produced by smoothing each crossing, respecting the orientation. This paper presents a satisfying combinatorial argument to show how any diagram can be altered to one of the same knot in which the Seifert circles are totally nested, without changing the number of Seifert circles. This gives a presentation of the knot as a closed braid, and leads to the result of the title. The algorithm for alteration of the diagram is straightforward, and gives a very practical way to represent the knot as a closed braid in explicit cases.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 4032620
zbMATH Keywords: braid index
zbMATH Keywords: Seifert circles of an oriented knot diagram
zbMATH Keywords: totally nested
zbMATH Keywords: knot
zbMATH Keywords: closed braid
reviewed by: H. R. Morton
MaRDI profile type: Publication
cites work: Braids and the Jones Polynomial
cites work: A new polynomial invariant of knots and links
cites work: Seifert circles and knot polynomials
description: scientific article; zbMATH DE number 4032620