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Given a diagram of a link  K  in  S  3 , we write down a Heegaard diagram for the branched‐double cover Σ( K ). The generators of the associated Heegaard Floer chain complex correspond to Kauffman states of the link diagram. Using this model, we make some computations of the homologyHF   ^   (  Σ  (  K  )  )    as a graded group. We also conjecture the existence of a  δ ‐grading onHF   ^   (  Σ  (  K  )  )    analogous to the  δ ‐grading on knot Floer and Khovanov homology.

A spanning tree model for the Heegaard Floer homology of a branched double‐cover