Khovanov module and the detection of unlinks

Understand

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 H_1/Torsion module structure on Heegaard Floer homology detects S^1xS^2 connected summands.