Making curves minimally crossing by Reidemeister moves
type: Item
instance of: scholarly article
title: Making curves minimally crossing by Reidemeister moves
zbMATH Open document ID: 0888.57001
author: Maurits de Graaf
author: Alexander Schrijver
published in: Journal of Combinatorial Theory. Series B
publication date: 1997-11-25T00:00:00Z
full work available at URL: https://ir.cwi.nl/pub/1361
review text: 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.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 57N35
zbMATH DE Number: 1076875
zbMATH Keywords: intersection
zbMATH Keywords: Reidemeister move
zbMATH Keywords: surface
zbMATH Keywords: regular system of curves
reviewed by: Jonathan A. Hillman
MaRDI profile type: Publication
OpenAlex ID: W2141665721
cites work: Q5580319
cites work: On the irreducible characters of Hecke algebras
cites work: Decomposition of graphs on surfaces
cites work: Algorithms for Jordan curves on compact surfaces
cites work: Teilungen der Ebenen durch Geraden oder topologische Geraden
cites work: Geometry of surfaces
DOI: 10.1006/JCTB.1997.1754
description: scientific article; zbMATH DE number 1076875