Loops in Reeb graphs of 2-manifolds
type: Item
instance of: scholarly article
title: Loops in Reeb graphs of 2-manifolds
zbMATH Open document ID: 1071.57017
author: Kree Cole-McLaughlin
author: Herbert Edelsbrunner
author: Vijay Natarajan
author: Valerio Pascucci
author: J. L. Harer
published in: Discrete \& Computational Geometry
publication date: 2005-02-11T00:00:00Z
review text: Let \(N\) be a compact connected surface of genus \(g\) with \(h\) boundary components and let \(f\) be a Morse function on \(N\). The Reeb graph of \(f\) is obtained from \(N\) by contracting the connected components of the level sets to points. The authors obtain sharp upper and lower bounds for the number of loops in the Reeb graph that depend on \(g\), \(h\) and the orientability of \(N\). The main result can be summarized as follows: When \(N\) is orientable, the number of loops is equal to \(g\) if \(h=0\) and is between \(g\) and \(2g+h-1\) if \(h\geq 1\); when \(N\) is nonorientable the number of loops is between \(0\) and \(g/2\) if \(h=0\), and is between \(0\) and \(g+h-1\) if \(h\geq 1\). The authors also give an algorithm for the construction of the Reeb graph in time O\((n \log n)\), where \(n\) is the number of edges in the triangulation used to represent the surface and the Morse function.
reviewed by: Mustafa Korkmaz
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 57R70
zbMATH DE Number: 2133695
zbMATH Keywords: 2-manifold, Reeb graph
zbMATH Keywords: Morse function
MaRDI profile type: Publication
full work available at URL: s00454-004-1122-6
OpenAlex ID: W2091452023
DOI: 10.1007/S00454-004-1122-6
description: scientific article; zbMATH DE number 2133695