The degree of the Alexander polynomial is an upper bound for the topological slice genus

We use the famous knot-theoretic consequence of Freedman’s disc theorem—knots with trivial Alexander polynomial bound a locally-flat disc in the 4-ball—to prove the following generalization. The degree of the Alexander polynomial of a knot is an upper bound for twice its topological slice genus. We provide examples of knots where this determines the topological slice genus.