A Concordance Invariant from the Floer Homology of Double Branched Covers

Ozsváth and Szabó defined an analog of the Frøyshov invariant in the form of a correction term for the grading in Heegaard Floer homology. Applying this to the double cover of the 3-sphere branched over a knot K, we obtain an invariant δ of knot concordance. We show that δ is determined by the signature for alternating knots and knots with up to nine crossings, and conjecture a similar relation for all H-thin knots. We also use δ to prove that for all knots K with τ(K) > 0, the positive untwisted double of K is not smoothly slice.