Rational Whitney tower filtration of links

TL;DR

This paper classifies links in the 3-sphere based on their Whitney tower filtrations in rational homology 4-balls, linking geometric structures to algebraic invariants like Milnor and Arf invariants.

Contribution

It provides a complete classification of links modulo Whitney towers in rational homology 4-balls and relates these to Milnor and higher order Arf invariants.

Findings

Complete classification of links in rational homology 4-balls

Geometric characterization of Milnor invariant vanishing

Insight into higher order Arf invariants and their role

Abstract

We present complete classifications of links in the 3-sphere modulo framed and twisted Whitney towers in a rational homology 4-ball. This provides a geometric characterization of the vanishing of the Milnor invariants of links in terms of Whitney towers. Our result also says that the higher order Arf invariants, which are conjectured to be nontrivial, measure the potential difference between the Whitney tower theory in rational homology 4-balls and that in the 4-ball extensively developed by Conant, Schneiderman and Teichner.