The minimal number of Seifert circles equals the braid index of a link
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.
Seifert circles of an oriented knot diagram
scientific article; zbMATH DE number 4032620