Khovanov Homology, Sutured Floer Homology, and Annular Links

Lawrence Roberts, extending the work of Ozsvath-Szabo, showed how to associate to a link, L, in the complement of a fixed unknot, B in S3, a spectral sequence from the Khovanov homology of a link in a thickened annulus to the knot Floer homology of the preimage of B inside the double-branched cover of L. In a previous paper, we extended Ozsvath-Szabo\u27s spectral sequence in a different direction, constructing for each knot K in S3 and each positive integer n, a spectral sequence from Khovanov\u27s categorification of the reduced, n-colored Jones polynomial to the sutured Floer homology of a reduced n-cable of K. In the present work, we reinterpret Roberts\u27 result in the language of Juhasz\u27s sutured Floer homology and show that our spectral sequence is a direct summand of Roberts\u27