Khovanov Homology, Sutured Floer Homology, and Annular Links J. Elisenda Grigsby and Stephan Wehrli

In [28], Lawrence Roberts, extending the work of Ozsváth and Szabó in [23], showed how to associate to a link, L, in the complement of a fixed unknot, B ⊂ S, a spectral sequence whose E term is the Khovanov homology of a link in a thickened annulus defined in [2], and whose E term is the knot Floer homology of the preimage of B inside the double-branched cover of L. In [6], we extended [23] in a different direction, constructing for each knot K ⊂ S and each n ∈ Z+, a spectral sequence from Khovanov’s 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’ result in the language of Juhász’s sutured Floer homology [8] and show that the spectral sequence of [6] is a direct summand of the spectral sequence of [28].