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 Arfinvariants, which are obstructions to framing a twisted Whitney tower in the
–ball bounded by a
link in the –sphere.
Applications include computation of the grope filtration and new geometric
characterizations of Milnor’s link invariants.
Keywords
Whitney tower, grope, link concordance, tree, higher-order
Arf invariant, higher-order Sato–Levine invariant, twisted
Whitney disk