A diagrammatical characterization of Milnor invariants
Abstract
The goal of this paper is to give a diagrammatical characterization of the information given by the Milnor invariants of links and string links. More precisely, we describe when two string links have equal Milnor invariants of length ≤ q and when a link has trivial Milnor invariants of lenght ≤ q. This will be done through the use of welded knot theory, involving the notions of arrow calculus and wq--concordance introduced by J-B. Meilhan and A. Yasuhara. These results is to be compared to the classification of links up to Cq--concordance obtained by J. Conant, R. Schneiderman and P. Teichner.
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