Combinatorial Approach to Milnor Invariants of Welded Links

Abstract

For a classical link, Milnor defined a family of isotopy invariants, called Milnor $\bar{\mathit{\mu }}$-invariants. Recently, Chrisman extended Milnor $\bar{\mathit{\mu }}$-invariants to welded links by a topological approach. The aim of this paper is showing that Milnor $\bar{\mathit{\mu }}$-invariants can be extended to welded links by a combinatorial approach. The proof contains an alternative proof of the invariance of the original $\bar{\mathit{\mu }}$-invariants for classical links.