Khovanov module and the detection of unlinks

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We study a module structure on Khovanov homology, which we show is natural under the Ozsvath-Szabo spectral sequence to the Floer homology of the branched double cover. As an application, we show that this module structure detects trivial links. A key ingredient of our proof is that the H₁/Torsion module structure on Heegaard Floer homology detects S¹xS² connected summands.