On the Heegaard Floer homology of singular knots and their unoriented resolutions

We investigate the Heegaard Floer homology for singular links using grid diagrams and study the effect that resolving a singularity has on the link Floer homology. In the main theorem, we find that the Heegaard chain complex for the resolved link has as its underlying module the direct sum of four copies of the chain complex for the singular link. The boundary map on this space is also a sum of the original boundary map acting on the analogous generators with the addition of an endomorphism. Although this correspondence between the chain complex for the resolution and four copies of the chain complex for the singular link does not respect the gradings and filtrations, even modulo two, we suggest an idea that might clarify the relationship between the gradings of these two chain complexes.