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 Λ*H1-module structure on Heegaard Floer homology detects S1 × S2 connected summands.