Milnor invariants, Orr invariants and slicing obstructions

I will give a proof of the Igusa-Orr theorem: Milnor invariants of order $\le 2k$ vanish on a link $L \subset S^3$ if and only if it is the boundary of a surface link $L'$ in $D^4$ such that the $(k+1)$th lower central quotient of $\pi_1(D^4\setminus L')$ is free nilpotent. The proof is based on Orr's $\theta$-invariants, which lie in the 3rd homology of certain free nilpotent groups. All definitions will be given. If time permits, I will also talk about hypothetical transfinite Milnor invariants and other slicing obstructions.