Khovanov homology and the Involutive Heegaard Floer homology of branched double covers

We use involutive Heegaard Floer homology to extend the Ozsváth-Szabó branched double cover spectral sequence relating a version of Khovanov homology and the Heegaard Floer homology of branched double covers. Our main tools are Lipshitz, Ozsváth, and Thurston’s reconstruction of the Ozsváth-Szabó spectral sequence using bordered Floer homology and Hendricks and Lipshitz’s surgery exact triangle in involutive bordered Floer homology.