Characterization(s) of the Reduced Peripheral System

Jean-Baptiste Meilhan (Université Grenoble Alpes)

The reduced peripheral system was introduced by Milnor in the 50’s for the study of links up to link-homotopy, i.e. up to homotopies leaving distinct components disjoint. This invariant, however, fails to classify links up to link-homotopy for links of 4 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. We give a topological characterization in terms of ribbon solid tori in 4-space up to link-homotopy, using a version of Artin’s Spun construction. The proof relies heavily on an intermediate characterization, in terms of welded links up to self-virtualization, providing hence a purely topological application of the combinatorial theory of welded links.

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