Localization spectral sequences for the knot floer homology of strongly invertible knots

We establish two spectral sequences in knot Floer homology associated to a directedstrongly invertible knot K: one from the knot Floer homology of K to a two dimen-sional vector space, and one from the singular knot Floer homology of a singular knotassociated to K to the knot Floer homology quotient knot of K. The first of thesespectral sequences is used to define a numerical invariant of strongly invertible knots.The second spectral sequence splits along the Alexander grading in a way that wepin down precisely