A combinatorial algorithm for immersed loops in surfaces
type: Item
instance of: scholarly article
title: A combinatorial algorithm for immersed loops in surfaces
zbMATH Open document ID: 1025.57025
DOI: 10.1016/S0166-8641(01)00202-4
author: Jane M. Paterson
published in: Topology and its Applications
publication date: 2002-12-17T00:00:00Z
review text: Starting with an arbitrary general position immersion of an oriented loop into a closed orientable surface, the author presents a combinatorial algorithm which homotops the loop to one with a minimal number of double points. The homotopy uses elementary Reidemeister-like moves. This approach is generalized to develop an algorithm which, given two homotopic immersed loops, homotops the first loop through a sequence of these elementary moves to produce a loop which is ambient isomorphic to the second. If both loops have \(k\) self-intersections, then the number of self-intersections remains equal to \(k\) throughout the conversion sequence. This gives an explicit homotopy that realizes a result of \textit{J. Hass} and \textit{P. Scott} [Topology 33, 25-43 (1994; Zbl 0798.58019)].
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 1846687
zbMATH Keywords: surfaces
zbMATH Keywords: immersions
zbMATH Keywords: loops
zbMATH Keywords: combinatorial
zbMATH Keywords: algorithm
reviewed by: James Hebda
MaRDI profile type: Publication
cites work: Q3025877
cites work: Intersections of curves on surfaces
cites work: Shortening curves on surfaces
description: scientific article; zbMATH DE number 1846687