Characterization of the reduced peripheral system of links

Benjamin Audoux; Jean-Baptiste Meilhan

doi:10.1017/s1474748023000543

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arXiv · 1904.04763

Characterization of the reduced peripheral system of links

Benjamin Audoux·Jean-Baptiste Meilhan

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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.

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Benjamin Audoux, Jean-Baptiste Meilhan. 2019-04-09. Characterization of the reduced peripheral system of links. https://doi.org/10.1017/s1474748023000543

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