More classes of stuck unknotted hexagons
type: Item
instance of: scholarly article
title: More classes of stuck unknotted hexagons
zbMATH Open document ID: 1072.51020
author: Greg Aloupis
author: Godfried Toussaint
author: Günter Ewald
published in: Beiträge zur Algebra und Geometrie
publication date: 2004-09-10T00:00:00Z
full work available at URL: https://eudml.org/doc/230244
full work available at URL: 6.html
review text: Allowing the vertices of a hexagon \(H\) in \(\mathbb{R}^3\) to move freely as long as the six edges do not cross or deform, the authors study the question how many connected components the space of \(H\) can have (for a suitable choice of the lengths of the edges of \(H\)). E.g., is each connected component of this space corresponding to a separate knot type, or does there exist some knot type (unknot) in separate components of the space? The authors consider the maximum number of embedding classes that any such unknot may have. Continuing respective investigations on hexagons in 3-space, they show that there exists an unknot for hexagons with at least nine embedding classes (before this paper, five was known to be a lower bound).
reviewed by: Horst Martini
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 52B10
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 2100232
zbMATH Keywords: connected components
zbMATH Keywords: embedding class
zbMATH Keywords: convex embedding class
zbMATH Keywords: trefoil embeddings
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2100232