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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.
Jesse Cohen (Thu,) studied this question.
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