Khovanov module and the detection of unlinks

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 Lambda* H-1 -module structure on Heegaard Floer homology detects S-1 x S-2 connected summands.