Making curves minimally crossing by Reidemeister moves
A regular system of curves on a surface \(S\) is a continuous map \(C:kS^1\to S\) which has no triple points and which is an embedding off a finite set of double points. The main result of this paper is that any such regular system can be transformed to a regular system with minimal intersections and self-intersections by a series of ``Reidemeister'' moves. Moreover, this can be implemented via a finite algorithm.
scientific article; zbMATH DE number 1076875