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We use the famous knot-theoretic consequence of Freedman's disctheorem---knots with trivial Alexander polynomial bound a locally-flat disc inthe 4-ball---to prove the following generalization. The degree of the Alexanderpolynomial 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.

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