An Ozsv\'{a}th--Szab\'{o}-type spectral sequence for links in $S^1× S^2$

We show that there is a spectral sequence with E²-page given by the Khovanov homology of a link in S¹× S², as defined by Rozansky in arXiv:1011.1958, which converges to the Hochschild homology of an A_∞-bimodule defined in terms of bordered Floer invariants. We also show that the homology algebras H_*hₙ of the algebras hₙ over which these bimodules are defined give nontrivial A_∞-deformations of Khovanov's arc algebras Hₙ for $n>1$.