• Motivation: Link homotopy
• Examples
• Questions asked by Milnor

• Chen-Milnor theorem on the nilpotent quotients of a link exterior fundamental group
• Magnus expansion of a longitude
• Indeterminacy and relations
• Examples

• Introduction to concordance
• Stallings' theorem on lower central series
• I-equivalence

We'll start the second part of the study group by recalling the perspective on the Milnor invariants presented in July: They try to decide (inductively) how deep longitudes of link components lie in the lower central series of the link group.

Milnor's algebraic algorithm for calculating presentations of quotients G/G_{n} of the link groups is computationally very expensive, and because of this prior to Tim Cochran's work not many explicit examples were available. Cochran's perspective via iterated intersection of Seifert surfaces yields a machine that given any desired Milnor invariant can cook up a link which realizes this.

In this talk I'll explain how trees can be used to package all Milnor invariants of a given length in one piece, and how you can realize any given first non-vanishing Milnor invariant by iterated Bing-doubling.