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

Abstract: We use involutive Heegaard Floer homology to extend the Ozsv\'ath-Szab\'o 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, Ozsv\'ath, and Thurston's reconstruction of the Ozsv\'ath-Szab\'o spectral sequence using bordered Floer homology and Hendricks and Lipshitz's surgery exact triangle in involutive bordered Floer homology.