A diagrammatical characterization of Milnor invariants

Boris Colombari

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arXiv · 2201.01499

A diagrammatical characterization of Milnor invariants

Boris Colombari

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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 $\leq q$ and when a link has trivial Milnor invariants of lenght $\leq q$. 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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Boris Colombari. 2022-01-05. A diagrammatical characterization of Milnor invariants. https://arxiv.org/abs/2201.01499

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