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Manolescu correction terms are numerical invariants of homology three-spheresarising from $\mathrm{Pin}(2)$-equivariant Seiberg-Witten theory that containinformation about homology cobordism. We discuss several constraints on theseinvariants for homology spheres obtained by Dehn surgery on a knot in thethree-sphere (and, more generally, in an integral homology $L$-space) in termsof the surgery coefficient, the concordance order, and the genus.

Manolescu correction terms and knots in the three-sphere