Estimating Matveev's complexity via crystallization theory
type: Item
instance of: scholarly article
title: Estimating Matveev's complexity via crystallization theory
zbMATH Open document ID: 1131.57023
author: Maria Rita Casali
published in: Discrete Mathematics
publication date: 2007-03-02T00:00:00Z
review text: The definition of Matveev's complexity \(c(M^3)\) of a \(3\)--dimensional manifold \(M^3\) is based on the existence of a \textit{simple spine} for \(M^3\) [\textit{S. V. Matveev}, Acta Appl. Math. 19, No.~2, 101--130 (1990; Zbl 0724.57012)]. In the paper under discussion the author studies Matveev's complexity by making use of another combinatorial description of \(M^3\), the so called crystallization. This allows to improve the known estimates of \(c(M^3)\) for manifolds given as a \(2\)-fold or \(3\)-fold simple branched covering over links in \(S^3\) as well as for \(3\)-manifolds given by Dehn surgery on a framed link in \(S^3\).
reviewed by: Michael Heusener
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M15
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M12
zbMATH DE Number: 5130426
zbMATH Keywords: Simple spine
zbMATH Keywords: Matveev's complexity
zbMATH Keywords: crystallization
zbMATH Keywords: branched coverings
MaRDI profile type: Publication
full work available at URL: j.disc.2006.07.021
OpenAlex ID: W2039802324
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DOI: 10.1016/J.DISC.2006.07.021
description: scientific article; zbMATH DE number 5130426