Localization and the Floer homology of strongly invertible knots

We establish two spectral sequences in knot Floer homology associated to a directed strongly invertible knot K: one from the knot Floer homology of K to a two dimensional vector space, and one from the singular knot Floer homology of a singular knot associated to K to the knot Floer homology quotient knot of K. The first of these spectral sequences is used to define a numerical invariant of strongly invertible knots.