Transfinite Milnor invariants of 3-manifolds

In his thesis, J. Milnor defined isotopy invariants of links, which determine when the lower central
series quotients of the fundamental group are free nilpotent.  It turned out that they are concordance
invariants, and finite type invariants in the sense of Vassiliev-Goussarov.  We generalize Milnor’s
invariants for 3-manifolds, using a homotopy theoretic approach, and we give an answer to a problem
asked by Milnor: find some method of attacking transfinite lower central series, and extracting invariants
from it.  This work is joint with Kent Orr.