A combinatorial description of knotted surfaces and their isotopies
type: Item
instance of: scholarly article
title: A combinatorial description of knotted surfaces and their isotopies
zbMATH Open document ID: 0870.57032
author: J. Scott Carter
author: Joachim H. Rieger
author: Masahico Saito
published in: Advances in Mathematics
publication date: 1997-08-28T00:00:00Z
review text: The authors' summary: ``We discuss the diagrammatic theory of knot isotopies in dimension 4. We project a knotted surface to a three-dimensional space and arrange the surface to have generic singularities upon further projection to a plane. We examine the singularities in this plane as an isotopy is performed, and give a finite set of local moves to the singular set that can be used to connect any two isotopic knottings. We show how the notion of projections of isotopies can be used to give a combinatorial description of knotted surfaces that is sufficient for categorical applications. In this description, knotted surfaces are presented as sequences of words in symbols, and there is a complete list of moves among such sequences that relate the symbolic representations of isotopic knotted surfaces''.
Mathematics Subject Classification ID: 57Q45
Mathematics Subject Classification ID: 57Q37
zbMATH DE Number: 1013822
zbMATH Keywords: knotted surfaces
zbMATH Keywords: isotopy
zbMATH Keywords: combinatorial
reviewed by: C. Kearton
MaRDI profile type: Publication
OpenAlex ID: W2082916529
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DOI: 10.1006/AIMA.1997.1618
description: scientific article; zbMATH DE number 1013822