We reformulate Heegaard Floer homology in terms of holomorphic curves in the cylindrical manifold † Œ0; 1 R, where † is the Heegaard surface, instead of Sym g .†/.We then show that the entire invariance proof can be carried out in our setting.In the process, we derive a new formula for the index of the @-operator in Heegaard Floer homology, and shorten several proofs.After proving invariance, we show that our construction is equivalent to the original construction of Ozsváth-Szabó.We conclude with a discussion of elaborations of Heegaard Floer homology suggested by our construction, as well as a brief discussion of the relation with a program of C Taubes.
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