Characterization of the reduced peripheral system of links
Geometric Topology
2024-11-20 v4
Abstract
The reduced peripheral system was introduced by Milnor in the fifties for the study of links up to link-homotopy, i.e. up to isotopies and crossing changes within each link component. However, for four or more components, this invariant does not yield a complete link-homotopy invariant. This paper provides two characterizations of links having the same reduced peripheral system: a diagrammatical one, in terms of link diagrams, seen as welded diagrams up to self-virtualization, and a topological one, in terms of ribbon solid tori in 4--space up to ribbon link-homotopy.
Keywords
Cite
@article{arxiv.1904.04763,
title = {Characterization of the reduced peripheral system of links},
author = {Benjamin Audoux and Jean-Baptiste Meilhan},
journal= {arXiv preprint arXiv:1904.04763},
year = {2024}
}
Comments
12 pages ; v2:names and surnames of the authors have been put in the right order, v3:an alternative proof for Lemma 1.16 has been given, v4:minor stylistic changes