  This note contains two remarks about the application of the d-invariant in
Heegaard Floer homology and Donaldson's diagonalization theorem to knot theory.
The first is the equivalence of two obstructions they give to a 2-bridge knot
being smoothly slice. The second carries out a suggestion by Stefan Friedl to
replace the use of Heegaard Floer homology by Donaldson's theorem in the proof
of the main result of Invent. Math. 192 (2013) no.3 717-750 concerning Conway
mutation of alternating links.
