Polynomial splittings of correction terms and doubly slice knots

Abstract

We show that if the connected sum of two knots with coprime Alexander polynomials is doubly slice, then the Ozsváth–Szabó correction terms, as smooth double sliceness obstructions, vanish for both knots. Recently, Meier gave smoothly slice knots that are topologically doubly slice, but not smoothly doubly slice. As an application, we give a new example of such a knot that is distinct from Meier’s knots modulo doubly slice knots.