A diagrammatical characterization of Milnor invariants

2022/01/05 by Boris Colombari, Colombari, Boris
Mathematics · #57K12 #57K16 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2201.01499

openalex publication_date 2022/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 w_q--concordance introduced by J-B. Meilhan and A. Yasuhara. These results is to be compared to the classification of links up to C_q--concordance obtained by J. Conant, R. Schneiderman and P. Teichner.

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