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The degree of the Alexander polynomial is an upper bound for the topological slice genus
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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.
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A note on the topological slice genus of satellite knots
The Z-slice genus of a satellite knot is at most the Z-slice genus of the pattern applied to the unknot plus the Z-slice genus of the companion knot.
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