On knot Floer homology in double branched covers

摘要

We define a link surgery spectral sequence for each knot Floer homology group for a knot, K, in a three manifold, Y. When K arises as the double cover of an unknot in S~3, and Y is the double cover of S~3 branched over a link, we relate the E~2-page to a version of Khovanov homology for links in an annulus defined by Asaeda, Przytycki and Sikora. Finally we examine the specific cases when the branch locus is a braid, and when it is alternating.