Construction of spines of two-bridge link complements and upper bounds of their Matveev complexities
type: Item
instance of: scholarly article
title: Construction of spines of two-bridge link complements and upper bounds of their Matveev complexities
zbMATH Open document ID: 1361.57011
author: Masaharu Ishikawa
author: Keisuke Nemoto
published in: Hiroshima Mathematical Journal
publication date: 2016-10-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1503.03599
full work available at URL: https://projecteuclid.org/euclid.hmj/1471024946
reviewed by: Biplab Basak
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M27
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 6643502
zbMATH Keywords: complexity
zbMATH Keywords: hyperbolic volume
zbMATH Keywords: triangulations
zbMATH Keywords: two-bridge links
MaRDI profile type: Publication
arXiv ID: 1503.03599
OpenAlex ID: W2963315750
Wikidata QID: Q128872465
DOI: 10.32917/HMJ/1471024946
review text: The notion of complexity was introduced by S. Matveev in 1990. This is now known as the Matveev complexity, and it is a very important invariant for 3-manifolds in geometric topology. But determining the Matveev complexity of a given 3-manifold is quite difficult in general. Thus, providing sharp bounds for the Matveev complexities of 3-manifolds is an important problem. In fact, many authors worked on this. In particular, Petronio and Vesnin gave a certain lower bound for the Matveev complexity of a two-bridge link complement.NEWLINENEWLINEIn this article the authors construct an almost-simple spine of a two-bridge link complement. This naturally gives upper bounds for the Matveev complexities of two-bridge link complements. Then using their construction together with the previous known lower bounds for the Matveev complexity of two-bridge link complements, they are able to determine the complexities for an infinite sequence of two-bridge links corresponding to the continued fractions of the form \([2,1,\dots,1,2]\). They also give upper bounds for the 3-manifolds obtained as meridian-cyclic branched coverings of the 3-sphere along two-bridge links.
description: scientific article; zbMATH DE number 6643502