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CHARACTERIZATION OF THE REDUCED PERIPHERAL SYSTEM OF LINKS

Published online by Cambridge University Press:  01 February 2024

Benjamin Audoux Open the ORCID record for Benjamin Audoux [Opens in a new window]  and
Jean-Baptiste Meilhan Open the ORCID record for Jean-Baptiste Meilhan [Opens in a new window]
Benjamin Audoux*
Affiliation:
Aix-Marseille Univ., CNRS, Centrale Marseille, I2M, Marseille, France
Jean-Baptiste Meilhan
Affiliation:
Univ. Grenoble Alpes, CNRS, Institut Fourier, F-38000 Grenoble, France (jean-baptiste.meilhan@univ-grenoble-alpes.fr)
*
benjamin.audoux@univ-amu.fr
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Abstract

The reduced peripheral system was introduced by Milnor [18] in the 1950s for the study of links up to link-homotopy, that is, up to homotopies leaving distinct components disjoint; this invariant, however, fails to classify links up to link-homotopy for links of four or more components. The purpose of this paper is to show that the topological information which is detected by Milnor’s reduced peripheral system is actually 4-dimensional. The main result gives indeed a complete characterization of links having the same reduced peripheral system, in terms of ribbon solid tori in 4–space up to ribbon link-homotopy. The proof relies on an intermediate characterization given in terms of welded diagrams up to self-virtualization, hence providing a purely topological application of the combinatorial theory of welded links.

Keywords

classical linkswelded linksribbon surfacesreduced peripheral systemsself-virtualization
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , First View , pp. 1 - 19
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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