This paper computes Whitney tower filtrations of classical links. Whitney
towers consist of iterated stages of Whitney disks and allow a tree-valued
intersection theory, showing that the associated graded quotients of the
filtration are finitely generated abelian groups. Twisted Whitney towers are
studied and a new quadratic refinement of the intersection theory is
introduced, measuring Whitney disk framing obstructions. It is shown that the
filtrations are completely classified by Milnor invariants together with new
higher-order Sato-Levine and higher-order Arf invariants, which are
obstructions to framing a twisted Whitney tower in the 4-ball bounded by a link
in the 3-sphere. Applications include computation of the grope filtration, and
new geometric characterizations of Milnor's link invariants.Comment: Only change is the addition of this comment: This paper subsumes the
entire preprint "Geometric Filtrations of Classical Link Concordance"
(arXiv:1101.3477v2 [math.GT]) and the first six sections of the preprint
"Universal Quadratic Forms and Untwisting Whitney Towers" (arXiv:1101.3480v2
[math.GT]