On a genus of a closed surface containing a Brunnian link
type: Item
instance of: scholarly article
title: On a genus of a closed surface containing a Brunnian link
zbMATH Open document ID: 1175.57009
author: Makoto Ozawa
published in: Tokyo Journal of Mathematics
publication date: 2009-04-21T00:00:00Z
review text: A link in the 3-sphere is called Brunnian if it is nontrivial but any sub-link obtained by removing a single component is trivial. In the paper under review, the author shows that if a Brunnian link of \(n\) components is isotoped so that it is contained in a closed embedded surface in the 3-sphere, then the genus of the surface is greater than \((n+3)/3\). A key lemma for the proof is the existence of a certain essential tangle decomposition for a Brunnian link, which is of interest independently. Using this lemma, the main result is proved via cut-and-paste techniques in a smart way. Also stated is a conjecture that the bound could be sharpened so that the genus of such a surface is greater than just \(n\).
reviewed by: Kazuhiro Ichihara
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57N05
zbMATH DE Number: 5545417
zbMATH Keywords: Brunnian link
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1233844057
OpenAlex ID: W2055313001
cites work: MORSE POSITION OF KNOTS AND CLOSED INCOMPRESSIBLE SURFACES
cites work: Sutured manifolds and generalized Thurston norms
DOI: 10.3836/TJM/1233844057
description: scientific article; zbMATH DE number 5545417