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's spectral sequence in a different direction, constructing for each knot K in S3 and each positive integer n, 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 Juhasz's sutured Floer homology and show that our spectral sequence is a direct summand of Roberts'.
Grigsby, J. Elisenda and Wehrli, Stephan M., "Khovanov Homology, Sutured Floer Homology, and Annular Links" (2009). Mathematics Faculty Scholarship. 121.
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