How to twist a knot
type: Item
instance of: scholarly article
title: How to twist a knot
zbMATH Open document ID: 0873.57009
published in: Archiv der Mathematik
publication date: 1997-11-02T00:00:00Z
review text: Take a strip of paper and ``twist'' it, tie a knot on it, and glue its ends together. Then you obtain a closed, twisted, and knotted strip. We use this as a model for a class of geometric objects which we call the class of closed strips. We define the twisting number of a closed strip which is an invariant of ambient isotopy measuring the topological twist of the closed strip. We classify closed strips in Euclidean 3-space by their knots and their twisting number. We prove that this classification exactly divides closed strips into isotopy classes. Using this classification we point out how some polynomial invariants for links lead to polynomial invariants for strip links. We give a method for knotting a strip with control on its twist, and our method includes a closed braid description of a closed strip. Finally, we generalize the notion of closed braids, allowing braids to be closed by any oriented knot and not only by the unknot.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 58D10
zbMATH DE Number: 1026260
zbMATH Keywords: closed strips
zbMATH Keywords: twisting number
zbMATH Keywords: polynomial invariants
zbMATH Keywords: links
zbMATH Keywords: closed braids
author: Thomas Randrup
author: Peter Røgen
MaRDI profile type: Publication
full work available at URL: s000130050055
OpenAlex ID: W2055580993
cites work: A polynomial invariant for unoriented knots and links
cites work: Knots
cites work: Q5331777
cites work: Q3993435
cites work: State models and the Jones polynomial
cites work: An Invariant of Regular Isotopy
cites work: Q4000283
cites work: Sides of the Möbius strip
DOI: 10.1007/S000130050055
Recommended article: Twisting Spun Knots
Recommended article: Twist-Roll Spun Knots
Recommended article: Twisting and knot types
Recommended article: On Twisted Knots
Recommended article: Q3378437
Recommended article: Knots
Recommended article: Q3409352
description: scientific article; zbMATH DE number 1026260