Khovanov homology, sutured Floer homology and annular links

摘要

In [28], Lawrence Roberts, extending the work of Ozsvath and Szabo in [22], showed how to associate to a link IL in the complement of a fixed unknot B∈S~3 a spectral sequence whose E~2 term is the Khovanov homology of a link in a thickened annulus defined by Asaeda, Przytycki and Sikora in [1], 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 [22] in a different direction, constructing for each knot K ∈S~3 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 Juhasz's sutured Floer homology [8] and show that the spectral sequence of [6] is a direct summand of the spectral sequence of [28].