On the Infinity Flavor of Heegaard Floer Homology and the Integral Cohomology Ring

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Ozsvath and Szabo construct a spectral sequence with E₂ term Λ*(H¹(Y;Z))⊗ Z[U,U⁻¹] converging to HF∞(Y,s) for a torsion Spinᶜ structure s. They conjecture that the differentials are completely determined by the integral triple cup product form via a proposed formula. In this paper, we prove that HF∞(Y,s) is in fact determined by the integral cohomology ring when s is torsion. Furthermore, for torsion Spinᶜ structures, we give a complete calculation of HF∞ with mod 2 coefficients when b₁ is 3 or 4.