Whitney towers and abelian invariants of knots

TL;DR

This paper connects classical abelian knot invariants like the Alexander polynomial, Blanchfield form, and Arf invariant to intersection data from Whitney towers in 4-dimensional space, offering a new computational approach.

Contribution

It introduces a novel relation between abelian invariants and Whitney tower intersection data, along with a new 3D algorithm for their computation.

Findings

Relates Alexander polynomial, Blanchfield form, and Arf invariant to Whitney tower intersections

Provides a new 3D algorithm for computing these invariants

Establishes a geometric interpretation of classical knot invariants

Abstract

We relate certain abelian invariants of a knot, namely the Alexander polynomial, the Blanchfield form, and the Arf invariant, to intersection data of a Whitney tower in the 4-ball bounded by the knot. We also give a new 3-dimensional algorithm for computing these invariants.