  Extending ideas of Hedden-Ni, we show that the module structure on Khovanov
homology detects split links. We also prove an analogue for untwisted Heegaard
Floer homology of the branched double cover. Technical results proved along the
way include two interpretations of the module structure on untwisted Heegaard
Floer homology in terms of twisted Heegaard Floer homology and the fact that
the module structure on the reduced Khovanov complex of a link is well-defined
up to quasi-isomorphism.
