#### Volume 17, issue 1 (2013)

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On knot Floer homology in double branched covers

### Lawrence P Roberts

Geometry & Topology 17 (2013) 413–467
##### Abstract

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.

##### Keywords
knot Floer homology, Khovanov homology, branched double cover
Primary: 57M27
Secondary: 57R58