Khovanov module and the detection of unlinks

Abstract

We study a module structure on Khovanov homology, which we show is natural under the Ozsváth–Szabó 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 ${\Lambda }^{\ast }{H}_1$–module structure on Heegaard Floer homology detects $S^1\times S^2$ connected summands.