Classification of welded links and welded string links up to w_q-concordance

Boris Colombari (Aix-Marseille Université)

The notion of w_q-concordance has been introduced by J-B. Meilhan and A. Yasuhara through the use of arrow calculus. It is a welded analogue of the C_k-concordance on classical links coming from the clasper calculus introduced by K. Habiro. In this talk I will present a classification of welded string links (resp. welded links) up to w_q-concordance by their Milnor invariants (resp. by their q-nilpotent peripheral system). I will compare these results to the classification of classical links up to C_k-concordance obtained by J. Conant, R. Schneiderman and P. Teichner before introducing the relevant invariants on welded objects. I will give elements of the proof of my results using a version of arrow calculus adapted to the representation of welded objects by Gauss diagrams.