k-reduced groups and Milnor invariants

Benjamin Audoux (1) , Jean-Baptiste Meilhan (2) , Akira Yasuhara (3)

1 I2M - Institut de Mathématiques de Marseille
2 IF - Institut Fourier
3 Waseda University [Tokyo, Japan]

We characterize, in an algebraic and in a diagrammatic way, Milnor string link invariants indexed by sequences where any index appears at most $k$ times, for any fixed $k\ge 1$. The algebraic characterization is given in terms of an Artin-like action on the so-called $k$-reduced free groups; the diagrammatic characterization uses the langage of welded knot theory. The link case is also addressed.

Domaines: Topologie géométrique [math.GT]

Benjamin Audoux, Jean-Baptiste Meilhan, Akira Yasuhara. k-reduced groups and Milnor invariants. 2022. ⟨hal-03691863⟩