A note on applications of the d-invariant and Donaldson's theorem

Abstract

This paper contains two remarks about the application of the [Formula: see text]-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 [J. E. Greene, Lattices, graphs, and Conway mutation, Invent. Math. 192(3) (2013) 717–750] concerning Conway mutation of alternating links.