Combinatorial Heegaard Floer homology and nice Heegaard diagrams

We consider a stabilized version of HF̂ of a 3-manifold YY (i.e. the U=0U=0 variant of Heegaard Floer homology for closed 3-manifolds). We give a combinatorial algorithm for constructing this invariant, starting from a Heegaard decomposition for YY, and give a topological proof of its invariance properties.