Whitney tower concordance of classical links

Abstract

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.

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])

References in corpus (4)

• Knot Concordance and Higher-Order Blanchfield Duality
• Characterization of Finite Type String Link Invariants of Degree < 5
• Tree homology and a conjecture of Levine
• Stable concordance of knots in 3-manifolds

Cited by in corpus (9)

• Universal quadratic forms and Whitney tower intersection invariants
• Stably slice disks of links
• Concordance of links with identical Alexander invariants
• Abelian quotients of the $Y$-filtration on the homology cylinders via the LMO functor
• Embedding surfaces in 4-manifolds
• Links Not Concordant to the Hopf Link
• On the kernel of the surgery map restricted to the 1-loop part
• Abelian quotients of the string link monoid
• Whitney tower concordance and knots in homology spheres