Representation of links by braids: A new algorithm (Q916146): Difference between revisions

Alexander's classical result shows that any oriented link can be presented as a closed braid. There have been a number of recent proofs of this result aimed at controlling the `complexity' of the braid in terms of the initial diagram of the link. The author presents a very simple and economical algorithm, which does not increase the number of Seifert circles, and which heavily limits the increase in the number of crossings. The elegant combinatorial proof is based on an analysis of the dual graph constructed from the dissection of the plane by the Seifert circles.