Distinguishing links up to link-homotopy by algebraic methods

In this paper we provide a complete algebraic invariant of link-homotopy, that is, an algebraic invariant that distinguishes two links if and only if they are link-homotopic. The paper establishes a connection between the “peripheral structures” approach to link-homotopy taken by Milnor, Levine and others, and the string link action approach taken by Habegger and Lin.